System method and apparatus for providing a load shape signal for power networks

ABSTRACT

A method, system and apparatus are provided for optimized load shaping for optimizing production and consumption of energy. Information signals indicative of a first load shape signal are obtained corresponding to a total load, a renewable energy load of one or more renewable energy sources and a non-renewable energy load of one or more non-renewable energy sources. The first load shape signal corresponding to renewable energy load is removed from a non-renewable energy load to obtain a resulting load shape signal. The resulting load shape is flattened signal by apportioning the resulting load shape signal across time intervals to obtain a flattened load shape signal. At least a portion of the first component corresponding to the renewable energy load is added to the flattened load shape signal to create an optimized load shape signal. The optimized load shape signal is provided to modulate electric loads of energy-consuming devices.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation in part of PCT application No.PCT/US2020/062467, filed on Nov. 26, 2020, which claims the benefit ofpriority to U.S. provisional patent applications 62/940,920 and62/940,922 both filed on Nov. 27, 2019, the contents of which areincorporated herein by reference for every purpose.

BACKGROUND OF THE INVENTION Field of the Invention

The application relates to managing or the management of energyresources, and more particularly to a power grid, from the supply side,to the demand side and/or the distributor side. The innovativesolution(s) in this application particularly are applicable but notlimited to managing or management of all energy resources includingrenewable energy resources in the power grid.

SUMMARY OF THE INVENTION

A method, system and apparatus are provided for optimized load shapingfor optimizing production and consumption of energy. Information signalsindicative of a first load shape signal are obtained corresponding to atotal load, a renewable energy load of one or more renewable energysources and a non-renewable energy load of one or more non-renewableenergy sources. The first load shape signal corresponding to renewableenergy load is removed from a non-renewable energy load to obtain aresulting load shape signal. The resulting load shape is flattenedsignal by apportioning the resulting load shape signal across timeintervals to obtain a flattened load shape signal. At least a portion ofthe first component corresponding to the renewable energy load is addedto the flattened load shape signal to create an optimized load shapesignal. The optimized load shape signal is provided to modulate electricloads of energy-consuming devices.

In another embodiment, the invention provides a load shaping signal to,for example, smart loads (such as appliances, electric vehicles (EVs),and EV chargers and the like), power utilities, power meters or smartmeters, distributors of power, and end users or their equipment.

It is useful to apply the various embodiments and their permutationsdisclosed above in terms of Hierarchies, which may be defined ascollections of loads. These hierarchies may be categorized loosely intodifferent geographic areas. Load shaping and providing a load shapingsignal or a plurality of such signals may be expressed in terms of thesehierarchies. The various hierarchies may be correlated to a sharing ofloads over a geographic or network area.

[Place Holder—Generic Definition of Global Hierarchy Generation of OLS]

Hierarchical Load Shaping Over 4-Geographies:

1. Wide (aka Global)-ISO service area: Maximize Renewables whileminimizing generation costs as already described. This overall objectivebenefits an Independent System Operator (ISO) or vertically integratedutility and is measured in reduced ops & maintenance costs (e.g. fuelcosts) and annual penetration of renewables (renewable kWh/total kWh).It shall be appreciated that the term global may refer to widegeographic areas such as a state, states or a country. The hierarchy maybe cross national boundaries.

To create a global OLS, take the forecast load, abstract the forecastrenewables to arrive at a net generation, which is then flattenedaccording to one or more techniques described above, and then add theforecast renewables back on the flattened shape to create the optimizedload shape signal.

It shall be appreciated that, on the global scale, statistics andforecasts even out and can be to a certain degree relied upon asaccurate for calculating the optimized load shape signal. On theregional or unit scale, statistics may not be as accurate. In otherwords, forecast error increases with decreasing time period andgeographic area. This is particularly true for determining instantaneousload shape signals, e.g., rather than seeking to determine a load shapeover a period of time, such as a year, which may be more accurate on thelocal scale.

2. Regional—which may be considered a utility or retailer service area:The objective in this case scenario is to minimize wholesale electricitypurchase costs, especially for retailers that operate at the regionallevel. A retailer for purposes of this disclosure is an entity that buyselectricity wholesale and sells electricity retail but may or may notproduce all or none of the electricity. As opposed to the global areawhere generators are main driver of economics, i.e., pay for theelectricity generation, in the regional scenario the main driver of theeconomics is the wholesale purchase cost of the electricity.

Retailers are especially concerned with maximizing their profits forselling energy, and can do so by minimizing the cost of wholesaleelectricity purchases. Retailers attract more customers if they selllower cost energy, and therefore seek to shape load at the customer endof the grid in order to reduce purchases of wholesale electricity athigh cost periods of time, such as off-peak times as opposed to on-peaktimes. In other words, retailers are motivated to buy energy at thecheapest price or during the cheapest price periods. Incontradistinction, generators are not buying energy as a rule, butgenerate energy or electricity and their main costs are infrastructure,operations and maintenance, particularly fuel costs.

The retailers or similarly situated entities, therefore, need an optimumload shape to manage load that minimizes the cost of purchasing thatenergy, in order to maximize profitability. Notably, this presumes thatthe retailers buy and sell energy as a single transaction, that is buyenergy with the intent or around the same period of time as selling theenergy. In other words, for the retailer or entity, the cost of buyingelectricity is linked directly to the price of selling that energy.

The retailer, therefore, seeks to purchase energy at the cheapest timeby managing the load of its customers such that the customer demandselectricity from the retailer at the cheapest time, thereby enabling theretailer to purchase the electricity cheaply. Thus, in one embodiment, amethodology is needed to link the optimum load shape to the price orwholesale price of energy. Put another way, the optimum or optimized(which is optimized in this aspect to save purchase costs) is based onthe price of energy for or over a period of time. In one aspect, theprice of energy may be forecasted, such as day-ahead pricing, or over aperiod such as hourly, or instantaneous meaning at or near moment energyprices.

In a more specific aspect, the invention provides the optimized loadshape signal based on the pricing of energy by inverting the price ofenergy. This may be the forecast wholesale pricing, or so-called realtime pricing that includes periodic pricing such as hourly pricing, orinstantaneous pricing. This objective benefits wholesale purchasers ofelectricity and is measured in reduced wholesale electricity procurementcosts. Retailers may also benefit from sharing load shapes with loadaggregators (e.g., Tesla, Honeywell, Nest, etc).

It shall be appreciated that the aspect of providing a modified pricingsignal as the OLS pertains not only to the retail situation but anywherethat the price of energy to the seller becomes important. It shall alsobe appreciated that the modification of the pricing or price of energymay be performed on a price in that moment or over time, and that theOLS may be obtained from parts of the price or pricing signal. Forexample, the price at a particular time may be used as a basis for alonger period of time, even though the actual price deviates somewhat.Alternatively, the load shape signal can be based on the price of energyaveraged over a period of time to generate the OLS. Alternatively, theload shape signal can be based on the price of energy weighted accordingto relative high and low demand, such that higher demand periods of timeare weighted such that the resulting load shape signal is lower, andhigher for when demand periods of time are lower.

Notably, in practice OLS energy management is described in terms ofpercentages. Therefore, in one aspect the price of pricing signal can bescaled to add up to unity and applied by using that percent in each partof a given time period. It is further notable that the modification ofthe OLS in this or other embodiments may be considered a simplificationof the OLS generation methodology.

3. Local—this hierarchy concerns the region of densely populated areas,for example, a city block. In a densely populated area, the grid'sconductors and transformers are not, in some areas, big enough to handleload especially where many users have high power needs, such as ownersof EVs who charge their cars at home and/or at the same time. Here, theobjective is to provide an OLS that is designed to prevent theoverloading of infrastructure, such as wires, conductors and/ortransformers serving the neighborhood. In contradistinction to theretailer situation, this solution benefits the end user customers andgrid infrastructure providers.

In urban settings, it is often the case that sensors are present in thearea that provide grid voltage and/or loading information. On thatbasis, the invention modifies the OLS to account for overloadsituations. For example, in an overload situation, the invention furtherprovides that the OLS for that period of time, i.e., during theoverload, the OLS is modified to reduce the energy consumption. Inparticular, during an overload situation the OLS is modified to, forexample, reduce the percentage of usage during that time by reducing theload by telling all the loads through the OLS to use a lesser load, thatis lower their demand or usage.

A meter or sensor may be situated upstream from the end user ormicro-grid that reports on voltages or voltages surges, or power orpower surges, and may be wired or wireless to communicate the voltage orpower remotely to another device. In this case, the invention may poll asensor or plurality of sensors and determine how to balance the load formultiple end users by providing a different load shape signal to eachend user or even a particular appliance or type of appliance, such as anEV.

In one embodiment, it is also possible to target appliances based onelectricity need or prioritization, such as emergency equipment athospitals. For example, the OLS could be modified for EVs in aparticular area, whereas the OLS for hospitals and their equipment isprioritized to have no reduction in usage. The same concept applies toother necessary services, such as fire services or police or emergencyresponse organizations.

In another embodiment, the modification of the OLS may be instantaneous,that is modified on the fly, or adjusted over periods of time, and mayfurther be based on the historical, empirical or forecast data of theparticular area. For example, the OLS for an area or particularappliance may be modified to reduce energy demand or load for a periodof time based on data from the logs of the usage for that area orappliance. Power quality sensors detect, predict, and then avoid hoursof congestion by applying a local OLS designed to mitigate congestion bykeeping load under congestion limits. The assumption is that anunderlying Locational Marginal Price (LMP) is available to invert andscale into a local OLS Shape.

This also reduces the cost of upgrading an area, that is to minimizedistribution grid upgrade capital expenditures, by applying OLS as anon-wires congestion mitigation in, for example, 200-home areas. Inother words, the cost of upgrading infrastructure is reduced ormitigated altogether. This objective benefits distribution utilities byproviding non-wires solutions to distribution congestion and is measuredin avoided wires-related infrastructure expense.

4. Hyper-local—referring to a smaller cross section of the grid, such asindividual residences, business, apartments, homes, or one or morebuildings. The objective here is to minimize grid-supplied electricitycosts ‘behind the meter’ in one or more buildings. This is done byproviding a link or an orchestration between the loads behind the meter,that is everything on the user side, such as the customer premiseswiring, the appliances, batteries, etc., on the user end. This objectivemay be thought of as creating a micro-grid behind the meter and benefitscommercial and residential retail electricity customers by ensuring allloads do not simultaneously energize (i. e., do not all come on at once)and is measured in reduced peak demand charges and usage duringhigh-price periods. Hyper-local load shapes can also ensure that batteryand other storage charge and discharge rates are not exceeded.

In one aspect, the invention may provide different load shapes to thevarious end users, or per appliance, so that they do not come on all atthe same time. In particular, the embodiment considers orchestrating theappliances behind a meter, or one end user, but may be applied of courseto multiple users. This is done by detecting the usage or on/off timesof the appliances and providing a different load shape for one or moreappliances at the end user. In the alternative, a single load shape maybe used for one end user, with portions that are modified, such asrepression or notching out of the single load shape at different times,according to different appliances such that one or more appliances donot come on (or fully come on) at the same time.

It shall be appreciated that the foregoing hierarchies are examples andone or more may be applied either singularly or in any combination, ormay be used on a system wide scale. Further, in any of the hierarchies,a flexibility parameter may be applied to the OLS. In some instances, itcan occur that the behavior of any given grid or microgrid becomesaccustomed to a given load shape and no longer responds to modification.For example, a group of end users who receive an inverted pricing signalas the load shape on one day, may in tato affect the entire load,thereby driving up prices for energy during that time, such as during anoff-peak period. In such a case, the OLS would need to be adjustedflexibly to take into account the inelastic limits of user behavior. Inanother example of inelasticity, the actual behavior and usage of energymay fall behind and may not accomplish the full OLS set for a particularperiod. In such instances, appliances may not be ready to demand energyat those times and degrees indicated by the OLS, such as when an EV maynot be plugged in at the time the OLS indicates the EV should becharging.

To resolve the foregoing inelasticity problems, for any givenenvironmental conditions, time of day, day of week/month, holiday,weather, etc., for a given load shape, the forecast load is expected tobe X, the optimized load shape is calculated according to X and resultsin Y as disclosed above in any of the embodiments, but the actual loadthat occurs on the grid or microgrid in the presence of the OLS signal Yis Z, which may or may not lie between X and Y. One option to resolvethis problem is to request more load or a portion or all of theremaining demand in another off peak period. Still another option is tolearn from the actual behavior and adjust Y to reflect the ability ofappliances and/or other end-uses to add or shed load at a given time.Such learning can be done over time, or by use of artificialintelligence or machine learning. In one aspect, an upper and lowerlimit can be determined or learned, wherein the lower limit is the mostamount of load that can be shed for a given period, and the upper limitis the maximum load that can be added for that area for a given period.The elasticity of load is a complex function of whether a number ofparticipating devices and other parameters such as weather, etc. (asstated above). The modification of the requested OLS (Y) may beiteratively adjusted, such that each difference between requested load Yand Z is adjusted closer to Z over time.

Z=f(X,Y)=Y ₂ =Y ₁+adjusted difference,

where Y₁ is the value of Y at time 1 and Y₂ is the value of Y at time 2.

In summary, the hierarchical design allows different load shapes andload shape generation schemes to be used in different geographies orlocations, that are nested geographically. In fact, one or more of theabove hierarchies can overlap, such as a Venn Diagram with global loadshapes encircling regional, local, and/or hyper-local shapes.Hierarchical nested shapes support the overall objective of embodiment(1) above as well as sub-objectives (2,3,4). It shall be appreciatedthat an opportunity cost exists based on the extent to which thebenefits of (2,3,4) reduce the benefits of (1). For example, thereduction in the overall global benefit of a local non-wires solution iscompared to the benefit of the reduced capital expense due to the localnon-wires solution. Of course, the above embodiments in the hierarchicalschema are not the entire set of ways to modify the OLS according togeography, network geography or location. The optimized load shape maysimply be referred to as the load shape or represented by the load shapesignal in any of the embodiments or combinations thereof.

BRIEF DESCRIPTION OF SEVERAL VIEWS OF THE DRAWINGS

The concepts described herein are illustrated by way of example and notby way of limitation in the accompanying figures. For simplicity andclarity of illustration, elements illustrated in the figures are notnecessarily drawn to scale. Where considered appropriate, referencelabels have been repeated among the figures to indicate corresponding oranalogous elements,

FIG. 1 illustrates and end-to-end power grid;

FIG. 2 are plots of the energy usage of different appliances;

FIG. 3 is a plot of wavelet decompositions and aggregated WARM-basedcurves;

FIG. 4 is a plot of the energy usage profile of RBSA homes;

FIG. 5 is a plot of the aggregate load profile of RBSA homes;

FIG. 6 is a heat map illustrative of energy usage of differentappliances;

FIG. 7 is a plot of a wavelet-based phase randomization simulation of anappliance;

FIG. 8 is a model of a building envelope expressed as a thermal network;

FIG. 9 is a map of the USA with different regional climatecharacteristics;

FIG. 10 is a plot of management of the optimization of an airconditioner;

FIG. 11 is a map of the USA showing residential electric rates;

FIG. 12 is a model showing variable production costs, emissions andelectricity flow per end user;

FIG. 13 is pictogram showing residential load shaping simulation of thepresent invention;

FIG. 14 is a state diagram of a hot water heater;

FIG. 15 is a map of Texas showing different environmental regions;

FIG. 16 is a flow diagram of the electric power according to differentweather zones;

FIGS. 17 and 18 are plots of actual and optimum power generation or loadshaping;

FIGS. 19 and 20 are plots of unshaped and optimum power generation orload shaping;

FIGS. 21 and 22 are plots of unshaped and optimum power generation orload shaping;

FIGS. 23 and 24 are plots of unshaped and optimum power generation orload shaping;

FIGS. 25 and 26 are charts of the actual/simulated total load versusactual/simulated net load;

FIG. 27 is a plot of simulated and actual loads;

FIG. 28 is a plot of simulated and actual loads;

FIG. 29 is a histogram of errors between simulated and actual loads;

FIGS. 30 and 31 are plots showing the base and reference demand of agroup of homes;

FIG. 32 is a plot showing the optimized demand; and

FIG. 33 are plots of load shapes showing the optimized load shapingsignal and appliance response for actual scenarios.

DETAILED DESCRIPTION OF THE ILLUSTRATED EMBODIMENTS

Automatic electric load shaping and subsequent modulation of power basedon shaping the load can increase the efficiency of existing thermalpower plants and facilitate a transition to carbon-free generation fromrenewables. The ongoing digitization of buildings, industry, andtransportation presents an ever-expanding set of opportunities to usethe Internet of Things to introduce load elasticity and alter thetraditional electricity supply-follows-demand paradigm. The solutionaddressed here is to create a globally applicable framework to model thevalue of flexible residential load across a range of geographies interms of electricity production cost and carbon dioxide emissions anddevelop a method system and apparatus to provide a load shaping signal,modify the load, and in so doing modulate the power generated by thermalpower plants and further to renewable energy sources. This inventionmodels an optimal supervisory control of residential building thermalmasses taking into account the complementary aspects of the modelpredictive control (MPC) of multiple degrees of freedom includingair-conditioning, electric domestic hot water heating, and batterystorage, and optimizes the load on the supply side.

The framework of the invention is capable of using, for example,historical load, weather, building stock attributes, operating schedulesof electrical devices, distribution feeder models, and generatorconstraints to quantify the value of residential load shaping fordecision and policymakers. Three phases or steps to complete the model:Phase or Step 1 is a data-driven model that analyzes, synthesizes,and/or statistically simulates diversity in residential load observed inempirical data associated with home appliances. Phase or Step 2quantifies feeder-wide electric grid benefits resulting from theaggregation of flexible loads, with time-of-day sensitivitiesinvestigated across electrical distribution networks, seasons, and U.S.climate regions. Phase or Step 3 estimates the system-wide impactslikely to result from jointly optimizing residential load with existinggeneration fleets and feasible penetrations of renewable generation inan annual case study of the large electric grid managed by the ElectricReliability Council of Texas. With the present invention a ⅓ reductionin annual generation costs and a ⅕ reduction in CO2 emissions at highrenewable energy penetrations results are possible.

As global agreements seek to reduce emissions and provide the world'spopulation with access to electricity produced without the combustion offossil fuels, a rapidly evolving set of generation, transmission,distribution, communications, and load management technologies arepoised to remake the energy landscape, creating a new energy paradigm.’Indeed, history shows that new forms of energy enable humandevelopments. Now more than ever, clean energy can deliver tangibleadvancements addressing the issues raised in Agenda 21 of the 1992United Nations Conference on Environment and Development and infollowing climate summits through the present day. Moreover, actionstaken today can bring much-needed innovation and security to the world'senergy systems, thereby offering opportunities for nations to providegeo-political and socio-economic leadership.

Specifically, increasing the penetration of clean and efficient RES(Renewable Energy Sources) can increase opportunities among the planet'simpoverished, with low-cost energy for the masses helping to erase thedividing lines between energy haves and have-nots, thus raisingproductivity and longevity. On an energy utility's supply side,electricity production costs vary as wind, solar, hydroelectric,conventional generators, and storage systems come on- and off-line tomeet customer demands. Variable generation cost is the primary driver inproduction cost, is directly proportional to the cost of fuel consumed,and is calculated based on a unit of electricity produced, e.g., amegawatt-hour.

On an energy utility's demand side, customers have costs associated withconsumption. For some uses, such as air-conditioning and heatingdomestic hot water (DHW), high energy costs may discourage consumption.For other uses, such as preparing a meal, the cost of energy may notinfluence consumption because people would rather pay higher energycosts even during peak times to feed themselves and family. Depending onend-use, cost and consumption may be correlated or may varyindependently as a function of time-of-day, day-of-week, season, desiredcomfort levels, and load management strategies such as the schedulingand control of appliances. Successful load management requires customereffort be minimal or better yet, non-existent, mostly seamless to theusers while saving them money.

Decreasing capital and operational costs are anticipated to drive solarand wind to further dominate the electricity generation mix.Accommodations for their variable and uncertain production of power willrequire new forms of system flexibility to assist in maintaining thecritical operational balance between generation supply and user demand.At low to medium penetration levels, in most countries, solar and windare the least expensive forms of marginal generation and drive costsdown by offsetting more expensive power from conventional generators.Conventional generators are still needed to provide base-load capacityand to cover periods of no sun or wind, along with the flexibility tofollow varying load.

At annual penetration levels of 7% to 27%, somewhat counter-intuitively,researchers at the National Renewable Energy Laboratory have shown thatgeographically dispersed multi-resource RES combined with (part-load)thermal generation has inherent flexibility which can help balancesupply and demand. At extremely high penetrations of RES, however, theamount of required system flexibility rises dramatically, potentiallymaking the marginal cost of 100% solar and wind generation prohibitivelyexpensive.

Buildings are likely contributors of grid flexibility and aresignificant users of energy, responsible for more than 73% of the totalelectricity usage in the U.S., with about 50% of that consumptionoccurring in residential buildings. In addition to buildings, theflexibility that can bolster the penetration and reach of RES is aspatiotemporal function of the types, location, and timing of user loadsand the grid resources that make up the ‘balance of system.’ As shown inFIG. 1, the balance of system refers to the types of conventional andRES generators, types of storage, types of loads, and the geographiclocations and connections of each to the grid.

FIG. 1 illustrates end-to-end generation-to-load system architecturereveals the balance of system when observed from any location. Forexample, when looking from a house, the balance of system is everythingbeyond the house. In FIG. 1, there is shown a power grid 100 with asupply side 102 that may include electric power generation plants, socalled power plants 110, which include traditional carbon based powergeneration units such as oil, gas, coal and nuclear as well as renewableenergy resources including hydroelectric, solar, and wind powergeneration units. The supply side 102 may also be considered to includethe infrastructure, including power distribution lines 103, such ashigh-tension lines, power lines or so-called transmission lines,transformers and substations (step up substations 107/step downsubstations 120 which may include a step down transformer 105). Thereare also distributors (not shown) that purchase power from traditionalpower generation firms to distribute power to consumers on the demandside or those that lease infrastructure and provide power from their ownpower generation equipment. There are also infrastructure firms thatprovide the infrastructure on the supply or demand side, such as thosethat provide software or apps to either test or regulate transmission ofpower or provide equipment such as smart meters or smart appliances, ornetwork boxes that measure or regulate the amount of power consumed by aconsumer or appliance. The supply side may also be referred to asupstream from the demand side. The demand side may provide power toelectric vehicles (EV) 109.

The demand side 104 is the consumer end that includes either residentialor private homes or business or company facilities or buildings, whichcan be considered as everything after the power leaves the transmissionlines. The demand side may also generate power, for example, from solarpanels or electric cars and can upload power into the power grid. In asense, these demand side power generation entities become suppliers ofpower. However, for purposes of this discussion we will refer to thoseas being on the demand side. Demand side entities and equipment shall bereferred herein as downstream of the supply side. As shown in FIG. 1, aload sharing apparatus may comprise a computing device 115, such as acomputer, having a processor 116 to run a computer readable medium 117,such as a computer program. The processor may be included in a computingdevice such as a smart switch, smart meter, thermostat, smart phone, anInternet router, a graphical user interface (GUI), cloud-based energycontroller, cloud appliance, data center, dashboard, home energymanagement system, a battery, an electric vehicle/electric vehiclecharger, an energy transformation device, water boiler, air conditioner,and an appliance

Many possible combinations of generation and load resources can achieveflexibility across the system. An essential requirement is the abilityof each to ramp up and down in concert with the others, within thecapacity constraints of the transmission and distribution or power grid.Exponential advances in the reach of telecommunications networks and thenumber of connected Internet of Things (IoT) devices together enable thesmart grid ever more capable of benefiting from residential loadflexibility; this long-held promising concept was the primary subject ofthis invention.

Using Internet-enabled distributed control, the evolving grid should beable to jointly optimize its own end-to-end efficiency. Throughautomatic residential load shaping (ARLS) that goes beyond traditionalpeak shaving demand response (DR), so that electric loads can beencouraged and discouraged throughout the day in order to modulatedemand and optimize the mix of available generation while maximizing theuse of RES and the security and reliability of the grid.

For over a decade, Internet-based feeds of the future costs ofelectricity have been used by commercial and industrial entities tomodulate demand, though have not been widely used at the residentiallevel. In the future, ARLS and home energy management systems (HEMS)could be critical for managing demand; for example, when spikes in loadoccur as many commuters begin charging their electric vehicles uponarriving at home or work. While communications networks and HEMS are notthe focus of this research, their increasing ubiquity and ease of useare assumed. Note that in the presence of intermittent Internetconnectivity, any HEMS must continue providing comfort and neededservices while attempting to reestablish communications with the grid.

Homeowners, in the absence of automatic load shaping, can manuallymanage electric loads, for example, vacuuming carpets when the sun wasshining to avoid the inefficiencies of battery charging and discharging.A software-based controller is needed that could maximize efficient useof energy by orchestrating user demand in concert with renewable energysupply, a battery, and a standby generator. On the news of highcurtailment of wind energy in Denmark and other countries, the vision ofthe software-based controller was extended to orchestrating supply anddemand on the electric grid.

To accelerate humankind's progress in replacing thermal power plantswith RES, the envisioned controller was further envisaged as part of atelecommunications-based system that would use the pricing ofelectricity to orchestrate energy supply and demand in order to maximizethe use of RES and the efficiency of power plants. Energy efficiency iscritical because, despite all renewable energy sources (RES),approximately 75% of the world's electricity is still generated usingvariants of the steam-electric Rankine Cycle first implemented in the18th century that is on average only 35-40% efficient. Thermal powerplants are expensive to operate, are the largest consumers of freshwater on the planet, and are among the largest producers of heat,producing nearly twice as much heat as they do electricity along withgreenhouse gas emissions that trap heat.

Modeling and simulating supply and demand in the electric grid is acomplex task. A simulation framework was created to analyze weatherforecasts, predict future electricity needs, and then prescribe futureelectricity prices that 1) favored RES, and 2) delayed the start-up ofthermal generators until they could operate at their maximum efficiency.As the Internet grew and software modeling tools became available itbecame possible to develop the necessary simulation framework toestimate the financial and emissions impacts expected by deployingdynamic electricity pricing over broad geographies and multiple climatezones. Dynamic pricing experiments provided excellent results in adeterministic model with three generators, but iterative approaches tomaximize the efficiency of the fleet of the 263 generators in Texassuffered from price-maker versus price-taker instabilities resulting inincreasing oscillatory load behavior. Generating feeder referencedemands ultimately inspired the development of an optimum load shapethat 1) met the objective of favoring RES, and 2) stabilized the load onthermal power plants so that they could operate most efficiently. Withthe possibility of highly penetrated utility-scale and distributed RES,savings in billions of dollars and trillions of pounds of CO2 emissionsare at stake worldwide on an annual basis.

As clean generation begets clean buildings, transportation, and industryand mitigates climate change, the simulation framework can identify theadditional savings attributable to ARLS supporting the increasedpenetration of RES. In layman's terms, what is missing in electric powergeneration and residential electrical use is something akin to the milesper gallon displays in automobiles that help drivers use fuelefficiently, in this case, an optimum load shape signal to help generateand use electricity efficiently. Also, missing are methods to estimatethe financial and emissions impacts attributable to jointly optimizingsupply and demand. These missing items were the motivation behind thisinvention. Through simulation, this invention investigated minimizingutilities' production costs by reducing the operation of the more costlythermal generators via centrally directed, distributed control ofresidential electric loads. Given Internet connectivity between supplyand demand, broadcast messages informed devices of electricity pricingor optimal load shapes based on generation constraints and theavailability of RES. In so doing, the traditional electric supply anddemand relationship was altered for devices participating in ARLS, withsupply no longer relegated to following demand, but rather, demandattempting to follow the lowest-cost forms of supply. That said, could acompelling financial case be made for ARLS, and if so, under whatconditions? Further, how might homes and appliances behave when addingor shedding electric load?

In the context of model predictive control (MPC), the on and off dutycycles of residential air-conditioning, domestic hot water (DHW)heating, and the charging and discharging of battery storage wereorchestrated to operate in concert with the balance of system in adistributed control paradigm that lowered the cost of generation whilemeeting user needs and maintaining user comfort. In addition toempirical data which helped inform DHW control opportunities essentialto facilitating the transition to demand following supply, wereend-to-end physical models that aided in exploring and quantifying thefinancial and emissions impacts through the programmatic exploration ofleast cost operating strategies across the distribution grids of anentire state.

As a proxy for the time-varying availability of low-cost electricity,load modulation either: 1) discouraged loads until lower-cost RES wereavailable or until conventional generation could operate mostefficiently, or 2) encouraged loads when RES was available. In differentexperiments, electricity pricing and load shape signals introducedelasticity into the traditionally inelastic residential electricitysupply and demand relationship in order to minimize the overallfinancial and environmental costs of generating electricity.

In combining generation, distribution, and load models, this researchestimated 1) the temporal upper and lower limits of ARLS for a summerday across the U.S., and 2) the annual impact on electricity producersin Texas in terms of variable generation costs and carbon dioxideemissions. Texas was chosen for this study as it is a multi-climate,large geographic area that can be modeled as an electrical island due toits limited imports and exports of electricity. Models based on hourlyand 5-minute intervals were used. Depending on the responsiveness ofresidential load, to a greater or lesser extent, top-down objectives toreduce generation costs and emissions were met by bottom-up loadshaping.

Out of the scope of this research, though included in the literaturereview, were: 1) Wholesale electricity markets and bidding mechanisms.2) Retail electricity tariffs and the associated processes that mightgovern end-user participation in ARLS. 3) Distribution ofparticipation-based credits or refunds, i.e., approaches forcompensating customers participating in ARLS. 4) Constraints on thetransmission grid that limited the flow of electric power. 5) Thedesign, operation, and integration of HEMS into ARLS.

Included in this chapter are reviews of the impact of RES penetrationand integration, power systems optimization in the face of variabilityand uncertainty, the importance of electricity financial market models,bottom-up dynamic pricing models, residential dynamic pricing behavior,residential DR load management, and model predictive control ofresidential electricity demand.

2.1 Impact of RES Penetration and Integration

This section starts with a review of forecast wind and solar penetrationand financial estimates and finishes with technical studies onintegrating RES. By some estimates, continuing deep declines in thecosts of wind, solar, and battery technologies will result in the globalgrid nearly half-powered on an annual basis by renewable energy sourcesby 2050. Some areas of the world are expected to have even higherpenetrations of RES due to advancements and deployments in transmissioninfrastructure. In 2019, the Bloomberg New Energy Finance (BNEF), NewEnergy Outlook estimated $13.3 trillion to be invested in new powergeneration capacity worldwide to 2050. Of this, 77% or $10.2 billion isexpected to go to renewables. Solar is expected to take $4.2 trillionand wind $5.3 trillion. Investment in renewable energy is expected toincrease to approximately $416 billion per year through 2050. Forecastsfor future penetration of RES suggest wind and solar will dominate thegeneration market. To put this in perspective, in 2018, two-thirds ofelectricity was generated by fossil fuels; by 2050 approximatelytwo-thirds of electricity is expected to come from carbon-freegeneration.

The primary driver of change most often cited is the levelized cost ofelectricity (LCOE), which is a measure of lifetime costs divided byenergy production. The LCOE from solar PV and wind continues to declineand is already lower than from conventional generation for two-thirds ofthe world's population. In the last year, the mean LCOE fromutility-scale PV technologies was down approximately 13%, the mean LCOEfrom onshore wind was down almost 7%, and the mean LCOE from offshorewind fell faster. The LCOE from PV is expected to fall 63% by 2050, toaround $25/MWh, module costs are down 89% since 2010 and are expected todecline another 34% by 2030. Underpinning declines in LCOE from PV arecost declines in solar technology. In addition, the levelized cost ofstorage is expected to decline across most use cases and technologies,especially for shorter duration applications. Lithium-ion remains theleast expensive storage technology and continues to decrease in cost dueto improved efficiencies and a maturing supply chain. To maximizebenefits to energy supply chain stakeholders and avoid issues such asover-generation, there will be an increasing need to develop microgridcontrol paradigms that programmatically optimize financial opportunitiesregarding when and how to buy, sell or curtail distributed PV, and howto maximize consumer savings by participating in ARLS.

In 2010, the first Western Wind and Solar Integration Study (WWSIS-1),prepared by General Electric for the NREL, was a landmark analysis ofthe operational impacts of high penetrations of wind and solar power onthe U.S. Western Interconnection. The study concluded that it wasfeasible for the region to accommodate 30% wind and 5% solar energypenetration with the caveat that 89 hours of the year had contingencyreserve shortfalls. A recommendation suggested that a DR program whichrequired the load to participate would be more cost-effective thanincreasing the spinning generation for each of the 8,760 hours of theyear.

While it is more difficult to explicitly calculate integration costs forwind and solar, total system costs with and without RES could becalculated with reasonably high confidence. In 2013, Phase 2 of theWestern Wind and Solar Integration Study (WWSIS-2) furthered the WWSIS-1study by calculating the wear-and-tear costs and emissions impacts offrequent cycling of fossil-fueled generators caused by thermal andpressure stresses during startup, load following, and shutdown. Theauthors concluded that wind and solar increased the annual cycling costsof fossil-fueled generators by $35-$57 million, or 13%-24%, across theWestern Interconnection, but paled in comparison to the annual savingsin fuel displaced by wind and solar of approximately $7 billion.

More recently, Phase 3 of the Western Wind and Solar Integration Study(WWSIS-3) furthered the WWSIS-1 and WWSIS-2 studies by investigatingfrequency response and transient stability of the North American grids.Of particular interest was the presence of wind and solar energypenetration that resulted in substantial changes to the characteristicsof the bulk power system, including different power flow patterns,different commitment and dispatch of existing synchronous generation,and different dynamic behavior of wind and solar generation. WWSIS-3 didnot identify any fundamental reasons why the Western Interconnectioncould not meet transient stability and frequency response objectiveswith 33% wind and solar generation on an annual basis.

Given the learnings in WWSIS-1, WWSIS-2, and WWSIS-3, how mightbuildings effectively participate in balancing the supply and demand ofelectricity in the presence of much higher penetration of RES? Allindicators in the literature were that wind and solar would continue togrow and would become the primary sources of power generation. With thepresent and future roles of wind and solar energy examined, a logicalfollow-up area of research was ascertaining the value of the flexibilityand optimization provided by ARLS in supporting increased penetration ofRES.

2.2 Power Systems Optimization in the Face of Variability andUncertainty

Power flow is the numerical analysis of the flow of electric power in aninterconnected system. Power flow analysis includes various aspects ofelectric power parameters, such as voltages, voltage angles, real power,and reactive power. Three operational power flow (OPF) models werereviewed.

A stochastic programming approach solved a multi-period OPF problemunder renewable generation uncertainty. The approach consisted of twostages. In the first stage, operating points for conventional powerplants were determined. The second stage incorporated the generationfrom renewable resources and optimally accommodated it by relying ondemand-side flexibility. The model used one generator along with wind asthe only RES, included a numerical solution, and was based on an hourlytimescale. Load DR was modeled as having 0 to 50% flexibility. The modelindicated a maximum reduction in mean wind spillage [MWh] as loadflexibility approached 20%.

An OPF model was used that determined power schedules for controllabledevices in a power network, such as generators, storage, and curtailableloads, which minimized expected short-term operating costs under variousdevice and network constraints. Schedules were chosen in a multistagedecision framework to include planned power output adjustments, orreserve policies, which tracked errors in the forecast of powerrequirements as they were revealed, and which could be time-coupled. Themodel used two generators along with wind as the only RES, included anumeric solution and a 2-bus network, though it did not specify atimescale. The model indicated a relative benefit of time-coupledresponse to uncertainty observed under different approximate treatmentsof the chance constraint, for different risk parameters. A real-timedistributed deferrable load control algorithm was proposed to reduce thevariance of net load (i.e., load minus renewable generation) by shiftingthe power consumption of deferrable loads to periods with high renewablegeneration. At every time step, the algorithm minimized the expectedvariance based on updated predictions. The model used wind as the onlyRES, included a system-level numeric solution, and used a 10-minutetimescale though did not include distributed generation or storage. Thealgorithm incorporated updated predictions about deferrable loads andrenewable generation to minimize the expected load variance goingforward. Qualitative insights from the analytic results were validatedusing trace-based simulations, which confirmed that the algorithm hadsignificantly smaller sub-optimality than optimal static control. Theliterature included coordinating electricity demand to meet supply, butat limited scale and complexity. Missing were large models of theend-to-end generation-to-load system incorporating multiple weatherzones, thermal models of buildings, hundreds of generators, thousands ofhomes, time-synchronous empirical load and RES data, and theconstruction attributes of building stock.

2.3 Importance of Electricity Financial Market Models

Local retail markets vary across states and utilities. Wholesale marketsvary across interconnect regions. Two market-based models were reviewed,and load adjustment was allocated to multiple consumers. They proposedand analyzed a simple uniform-price market mechanism where everyconsumer submitted a single bid to choose a supply function from a groupof parameterized ones. The parameterized supply functions were designedto ensure that every consumer's load adjustment was within an exogenouscapacity limit that was determined by the current power system operatingcondition. The model included a system-level numeric solution, though itdid not include RES, distributed generation or storage, and did notspecify a timescale. The proposed uniform-pricing mechanism achievedsocial optimality at a competitive equilibrium.

Coordination of a population of residential electric thermostaticallycontrolled loads (TCLs) with unknown parameters, was studied to achievegroup objectives. The problem addressed involved designing the devicebidding and market clearing strategies to motivate self-interested usersto realize efficient energy allocation subject to a peak energyconstraint. The model did not include a numeric solution, RES,distributed generation or storage, and did not specify a timescale. Amechanism was proposed to implement the desired social choice functionin a dominant strategy equilibrium. It was shown that under the proposedmechanism, the coordinator could not only maximize the social welfarebut could also realize the team optimal solution. From the literature,it was concluded that electricity financial markets could make or breakbusiness cases for increasing penetration of RES.

2.4 Bottom-Up Dynamic Pricing Models

While top-down models can provide important insight, they are acomplement to and not a replacement for bottom-up data-driven models.Two studies from University College Dublin were explored to assess thebenefits of bottom-up modeling. McKenna and Keane presented a bottom-upload model coupled with a novel methodology to capture the discrete,bounded, and uncertain consumer response to variable prices. The modelused Monte Carlo simulation techniques and price elasticity matrices toaffect the probability of consumption, taking into account detailedconsumer characteristics and appliance operation. The model ran ahigh-resolution simulation of residential load response and quantifiedbehavioral changes using standard load metrics. The model includedself-elasticity and cross-elasticity coefficients at different timeintervals. A step-change in electricity price resulted in both intra-and inter-temporal changes in electricity demand, illustrating that DRcan be a reaction to current, upcoming, and past prices. Modelaggregation was limited to the distribution network with a note thattransmission and distribution peaks on each are independent and notnecessarily coincident (though often are coincident in the U.S. andelsewhere).

In their subsequent paper, McKenna and Keane presented a comprehensivelow-voltage residential load model of price-based DR. High-resolutionload models were developed by combining Monte Carlo Markov Chainbottom-up demand models, hot water demand models, discrete state-spacerepresentation of thermal appliances, and composite time-variantelectrical load models. Price-based DR was then modeled through controlalgorithms for thermostatically controlled loads, optimal scheduling ofwet appliances, and price elasticity matrices for the inherently elasticresponse of the consumer. The developed model was used in a case studyto examine the potential distribution network impacts of theintroduction of dynamic pricing schemes. The effects of cold loadpick-up, rebound peaks, decrease in electrical and demand diversity, andimpacts on loading and voltage were presented. From the literature, itwas concluded that changes in electricity demand due to dynamic pricingcan be difficult to model.

2.5 Residential Dynamic Pricing Behavioral Review

It was found utilities were showing increasing interest in residentialDR. It was posited that residential DR can be treated as an energyresource which can be assessed and commercially developed whilerecognizing there are still some issues that remain to be addressed forDR to be successful. These included the price unresponsiveness of someresidential consumers, equity issues, and the high cost of the meteringinfrastructure. It was investigated and presented some of the challengesin achieving effective voluntary demand reduction based on reviews ofliterature in residential DR and energy use behavior. The use of ahybrid engineering approach was considered using social psychology andeconomic behavior models to overcome these challenges and to realize thebenefits of supply security and cost management.

Lessons on how to encourage households to adjust energy end use throughdynamic tariffs were also looked at. They identified four hypothesesrelated to fostering DR through dynamic tariff schemes and examinedwhether these hypotheses could be accepted or rejected based on a reviewof published findings from a range of European pilot projects. Theyqualitatively concluded that dynamic pricing schemes have the power toadjust energy consumption behavior within households (this is not asurprise) but did not provide quantitative estimates. In order to workeffectively, they recommended that a dynamic tariff should be simple tounderstand for the end-users, have timely notifications of pricechanges, and have a considerable effect on their energy bill.Additionally, if the tariff was complex, that the burden for theconsumer should be removed by introducing automated control. Althoughsometimes the mere introduction of a dynamic tariff was proven to beeffective, often the success of the pricing scheme also depended onother factors influencing the behavior of end-users. An essentialcondition to make dynamic tariffs work successfully was that theend-users should be engaged with them.

A review of North American studies of DR strategies suggested that themost effective strategy to date was a critical peak price CPP) programwith enabling technology to automatically curtail loads on event days.The authors found there was little evidence that automated CPP causessubstantial hardship for occupants, especially if they had input intowhich loads were controlled, understood how they were controlled, andhad an override option. In such cases, a peak load reduction of at least30% was a reasonable expectation, though the calculation was unclear.The authors posited that it might be possible to attain such loadreductions without enabling technology by focusing on household typesthat are more likely to respond and providing them with excellentsupport. Per the authors, in comparison to CPP, which would only be useda few days per year, a simple time-of-use daily program could onlyexpect to realize on-peak reductions of 5%.

An overview of the literature on residential DR systems, load schedulingtechniques, and the latest information and communication technologiesthat support residential DR applications was also looked at. Challengeswere highlighted, analyzed, and were likely to become relevant researchtopics concerning residential DR. Their literature review showed thatmost DR schemes suffer from a price-maker versus price-taker externalityproblem that involves the effect of high-level customer consumption onthe price rates of other customers, especially during peak periods. Arecommendation for using an adaptive multi-consumption level pricingscheme was presented to overcome this challenge.

In summary, for several decades, there has been much discussion anddebate of the appropriateness and effectiveness of dynamic residentialpricing of electricity. Popular questions have included 1) Are automatedHEMS necessary? 2) What incremental price changes and absolute pricesare fair to consumers and result in optimal system performance? 3) Whilereacting to price changes, will all appliances become synchronized inturning on and off, and if so, how severe are synchronization andrebound effects?

2.6 Residential Demand Response Load Management

Typically, DR is sparsely deployed and only used a few times a year, forexample in high-risk transmission-constrained geographies, such as theFlorida mainland peninsula where coastlines limit transmission ofelectricity to a relatively narrow corridor for hundreds of miles.Despite most customers saying they want the ability to control theirenvironment, and most reacting negatively to the thought of thedraconian “Big Brother” intrusions described by Orwell, today, millionsof homeowners in Florida and elsewhere accept monetary incentives inexchange for allowing utilities to shut off their appliances. The neteffect is that customers give up control at unknown times regarding therelative priorities and timing of specific appliance operations. Theremainder of this section is an illustrative example of a current DRprogram that has remained mostly unchanged since the author visited andstudied DR programs at Florida Power and Light Company (FPL) in 1990while contracting to jointly provide FPL and Bell South Communicationswith next-generation energy management gateway technology.

Then and now, approximately 52% of the total demand for energythroughout the FPL service territory comes from the residential sector,of which approximately 30-40% is directly related to air-conditioning.FPL is a U.S. energy utility that offers DR through their ‘On Call’direct load control program which started in the 1980s and has over amillion customers currently enrolled. Customers who volunteer toparticipate in On Call assist FPL in meeting the energy needs of allcustomers when demand for electricity is highest. In exchange for theirwillingness to shed load without notice, participating customers receivea credit on their electric bill when they agree to let FPL turn off theequipment that each customer specified when enrolling in the On-Callprogram. How On-Call works: An FPL electrician installs a smallenergy-management device (a radio-controlled relay) on equipment thatcustomers' select, including swimming pool filtration pumps, waterheaters, and air conditioners. FPL may occasionally switch-off selectedequipment remotely for short periods during extremely high electricitydemand such as a summer afternoon with higher than forecastedtemperatures. Customers receive a monthly credit on their bill even ifFPL never switches off their equipment totaling up to $137 annually,depending on the equipment and program options that customers selected.

The real-time disabling of appliances used by FPL, Duke PowerCorporation, Potomac Electric Power Company and others, typically usesone-way (utility to home) radio frequency communication systems toremotely control appliances. Existing systems have at least twoshortcomings: 1) Perhaps because of fear of occurring like Big Brother,they are rarely used and hence only provide benefit during extremecrises when customers' demand for electricity is expected to exceed thepower utility's supply. 2) They are limited in function because theyonly defer customer loads to a later time. These systems can neitheranticipate individual customer loads nor schedule such loads to operate“ahead of time” to favor RES and improve the efficiency of generation.While numerous forms of customer load management have been developed anddeployed over many decades, relatively crude DR programs have enduredand remain the norm in modern times. Despite the rapid growth of in-homeInternet-connected devices, residential DR load management remains arelative niche solution to the increasing threat of utility brownouts,blackouts, and escalating costs. Given the recent rapid growth ofIoT-enabled home security and home automation, it is conceivable thatgrid-tied HEMS offerings may significantly expand the geographicfootprint of DR programs. While it remains unclear when this mighthappen, drivers of change likely include increasing grid failures due toaging infrastructure and severe climate conditions, such as extreme heatand storms.

Several outstanding questions remain when looking toward the future.What potential migration paths enable much more frequent (intra-day) useof DR? What evaluation strategies might make sense in order to includeappliances other than pool pumps, air conditioners, and DHW heaters? Howmight emergency systems be used, for example during Hurricanes, inconjunction with real-time load flexibility? Additional models discussedin the literature section of Chapter 4 include modeling residentialdemand and DR. Based on the needs identified during a review of theliterature, the directed distributed control paradigms proposed in thisinvention seeks to provide continuous load shaping that overcomes theshortcomings of existing DR load management systems.

2.7 Model Predictive Control of Residential Electrical Demand

In this section are results of searching the literature for frequent,transactive, intraday, consumer-configurable load shaping for batteriesand storage-capable TCLs including heating, ventilation, andair-conditioning (HVAC), refrigerators, freezers, and DHW heaters. Astochastic model predictive control strategy for the climate control ofbuildings that takes into account weather predictions to increase energyefficiency while respecting constraints resulting from desired occupantcomfort was studied. For selected cases, the stochastic model predictivecontrol approach was analyzed in detail and shown to outperform currentcontrol practice significantly. This work was extended by addingMPC-based window blind positioning and electric lighting such that theroom temperature, as well as CO2 and luminance levels, stayed withingiven comfort ranges. What is missing in their papers are the controlsof additional degrees of freedom such as TCL appliances and batterystorage.

Predictive control solutions reduce the energy usage of buildings,improve occupant comfort, and reduce peak electricity demand. The focuswas on the automated optimal control of blinds, electric lighting,heating, cooling, and ventilation in individual building zones. Projectresults were: software, models, and data sets for the simulation-basedassessment of building control; new algorithms for improved weatherpredictions at a building's location; analysis of energy-savingpotentials related to control; novel control algorithms; and preparationof a demonstration project in a representative office building.

Coordinating regulation and DR in electric power grids uses multiratemodel predictive control and a framework for reducing supply-demandimbalances in the grid by jointly controlling both the supply-sideelectric power regulation together with the demand-side energyconsumption by residential and commercial consumers' DR. Their focus wason performance improvements that arise from the complementary dynamics:Regulation allows for frequent control updates but suffers from slowerdynamics; DR has faster dynamics but does not allow as frequent controlupdates. They proposed a multirate MPC approach for coordinating the twoservices and referred to this coordinator as an aggregator. MultirateMPC captured the varying dynamics and update rates, and nonlinearitiesdue to saturation and ramp rate limits, and a total variation constraintlimited the switching of the DR signal. Their approach could operatewith both direct reference or an indirect market price-based imbalancesignal. Numerical examples were presented to show the efficacy of thisjoint control approach.

The impact of large-scale distributed residential HVAC controloptimization on electricity grid operation and renewable energyintegration was assessed. They concluded that using distribution networkpower flow simulation, the results of the controller's actions could beassessed at the distribution feeder level to evaluate the aggregateimpact on feeder demand. Three combinations of feeders and climates,representing several typical of those found in the United States, werestudied. The work further considered the ability of the methodology toaddress feeder demand variability introduced when large amounts of solarand wind generation were present. Their work is a point of departure forthis invention.

Building-to-grid integration was investigated through commercialbuilding portfolios simultaneously participating in both energy andfrequency regulation markets. A model predictive control framework wasproposed to determine optimal operating strategies in consideration ofenergy use, energy expense, peak demand, economic DR revenue, andfrequency regulation revenue. The methodology was demonstrated throughsimulation for medium office and large office building applications,highlighting its ability to merge revenue-generating opportunities withtraditional demand and cost-reducing objectives. This did not includegrid modeling. MPC research has been informed by research in commercialbuilding dynamics, sensitivity analysis, and load profiles wasperformed. Foresee™, a user-centric home energy management system couldhelp optimize how a home operates to concurrently meet users' needs,achieve energy efficiency and commensurate utility cost savings, andreliably deliver grid services based on utility signals. Foresee wasbuilt on a multi-objective model predictive control framework, whereinthe objectives consisted of minimizing energy cost and carbon emissionswhile maximizing thermal comfort and user convenience. Foresee learneduser preferences on different objectives and acted on their behalf tooperate building equipment, such as home appliances, photovoltaicsystems, and battery storage. In this work, machine-learning algorithmswere used to derive data-driven appliance models and usage patterns topredict the home's future energy consumption. This approach enabledhighly accurate predictions of comfort needs, energy costs,environmental impacts, and grid service availability. Simulation studieswere performed on a subset of field data from a residential buildingstock data set collected in the Pacific Northwest. Results indicatedthat foresee generated up to 7.6% in whole-home energy savings withoutrequiring substantial behavioral changes. When responding to DR events,foresee was able to provide load forecasts upon receipt of eventnotifications and delivered the committed DR services with 10% or fewererrors. Foresee fully utilized the potential of battery storage andcontrollable building loads and delivered up to 7.0-kW load reductionsand 13.5-kW load increases. These benefits were provided whilemaintaining the occupants' thermal comfort and convenience in usingtheir appliances. The exciting work neither included grid modeling northe results of aggregating multiple homes.

A methodology to integrate both the building occupants andbehavior-based approaches into the design of the energy managementsystem was considered. Occupant behavior was modeled using randomvariables and influenced energy management via a disturbance feedbackpolicy. For the future investigation, other aspects of behavior beyondtemperature bounds, e.g., controlling occupancy or other internal gains,humidity, lighting, could be considered. The statistical approachadopted could be replaced with a more sophisticated user-specificdata-driven approach.

In summary, MPC is an advanced control technique which, when applied tobuildings, employs a model of the building dynamics and solves anoptimization problem to determine the optimal control inputs. Thoughmuch of the work on model predictive control has focused on commercialbuildings, some research has focused on residential applications, thesubject of this research. While industrial and commercial-scale loadshaping and modulation are more developed and mature, to date,literature searches have returned a scarcity of system-level modelscovering the end-to-end impact and value of residential applications ongeneration and distribution. No models were found estimating the valueof whole-house load shaping to generation when coupled with highlypenetrated utility-scale RES, distributed PV generation, and batterystorage. Instead, found were a plethora of subsystem models with alimited or unspecified spatial and temporal resolution. Some of the morerelevant work included efforts to simulate the drivers of residentialdemand (i.e., the loads) that could be managed by ARLS. Of particularinterest was literature covering the modeling of utility transmittersand residential receivers operating together in a distributed controlparadigm. A primary goal of reviewing the literature was finding modelsthat quantified how residential thermal and electrical storage couldcontribute to raising or lowering aggregate demand when responding toload shaping signals intended to raise the utilization of variablerenewable generation and increase overall system efficiency. Results ofthe review suggested that nascent developments in modeling paradigmsthat leverage a combination of applications such as PLEXOS, GAMS,GridLAB-D, and GridMPC, held promise in assessing the system-levelimpact of residential load flexibility.

Chapter 3

Methodology Development

This chapter extends the review of past work and relevant topics.Included are the research points of departure, differences from citedwork, research hypotheses, and an outline of the research performed. Theprimary goal in methodology development was the assembly of a simulationframework for estimating the potential impacts and value of ARLS acrossa range of geographies and climates in order to provide results ofinterest to decision and policymakers and to an those with interest infunding further development of this work.

3.1 Research Point of Departure

Much of the research cited in the literature review collectivelyprovided a point of departure for the work described in this invention.From the perspective of choosing physical models, the work on GridMPCprovided a basis for a thermal building model and a solar model. Thework on GridLAB-D and on grid taxonomy provided a basis for thedistribution grid model. The NREL buildings group provided a basis forthe electric DHW heater model. The work provided a basis for developinga battery storage model from first principles.

Specifically, a point of departure in the following areas 1) From aspatial perspective, in order to simulate a large geographic area, anopportunity existed to extend the prior analysis from one electricaldistribution feeder in each of three cities to a full complement of 48feeders across eight cities. 2) From a temporal perspective, in order toprovide annual estimates, an opportunity existed to extend the prioranalysis from one month to an entire year. 3) From a weatherperspective, in order to provide historical estimates and future basedscenarios, an opportunity existed to include an alternative weatherinput mechanism for importing actual or simulated weather station data.4) From a degree of control perspective, in order to simulate the MPC ofother significant uses of residential electricity, an opportunityexisted to extend the GridMPC particle swarm optimization (PSO) controlalgorithm from air conditioning to include electric DHW heating andbattery charging. 5) From the perspective of evaluating the impact ofincreasing RES, in order to model high penetrations of wind and solarenergy, an opportunity existed to leverage the methods of in calculatinghouse and feeder level energy uses and flows. 6) From a metricsperspective, in order to include measures of load shaping effectiveness,an opportunity existed to add a new percent load shaped metric foranalysis of houses, feeders, and larger geographies. 7) From a loadshaping perspective, in order to evaluate the efficacy of alternativeshaping strategies, an opportunity and working environment existed toexperiment with electricity pricing and optimal load shapes.

In order to inform GridMPC of the usage diversity observed in empiricaldata, the RBSA dataset provided opportunities for data-driven analysisof over two-years of 15-minute observations of significant uses ofresidential electricity. Note that disagreement between RBSAobservations and GridLAB-D usage schedules resulted in adjustments toimprove the fidelity of the electric DHW heater energy usage model.

From the perspective of evaluating the state of the art in residentialDR and price response mechanisms, literature reviews providedperspectives in DR capabilities vis-à-vis the continuous ARLS approach.From the perspective of evaluating practical implementations ofresidential DR, in addition to behavioral review, the Florida Power andLight Company ‘On Call’ program provided a typical example of anenduring residential DR program. From the perspective of creating andwidely deploying a paradigm shift in DR capabilities, it is interestingto note that 1) over 30 years, little has changed in the On-Callprogram, and 2) DR programs are not commonplace. From the perspective ofcalculating variable generation cost and CO2 emissions, the GAMSsoftware and methods provided the basis of a model for simulating theunit commitment of the Texas electric power generation fleet. After muchdiscussion and consideration, the methods considered provided theinspiration and underpinnings for the concept of a daily optimum loadshape.

3.2 Research Hypotheses

The objective of this research was to estimate the value of loadflexibility in support of maximizing the use of low-cost RES andminimizing the present worth life-cycle costs of generating electricityfor residential customers. The orchestration of fossil and RESgenerators and distributed thermal and battery storage operating inconcert with the balance of system were explored. The core conceptsbehind this research were formulated into three hypotheses that provideddirection and structure to investigating the value of jointly optimizingelectric power generation and residential electricity use.

3.2.1 Hypothesis 1: Data-driven models improve load simulation.Data-driven analysis of empirical electricity usage data fromair-conditioning and appliances can aid in quantifying and simulatingdiversity in residential electric loads. While studying Probability andStatistical Methods for Natural and Engineered Systems, and AdvancedData Analysis Techniques, unsatisfying results were obtained fromapplying data-driven stochastic approaches to quantify and simulate theenergy usage diversity observed in the empirical data from the NorthwestEnergy Efficiency Alliance (NEEA), Residential Building Stock Analysismetering study (RBSA). Specifically, traditional regression techniquesfailed to reflect both diversity and non-stationarity in energy usageamong homes and appliances. This hypothesis was motivated by the need tounderstand the level of diversity in energy usage as observed inreal-life situations, a critical requirement for realistic simulation ofthe benefits of load flexibility. Please see Chapter 4 for furtherdetails.

3.2.2 Hypothesis 2: MPC models, informed by diversity, can aid inquantifying end-to-end system benefits of load flexibility. Modelpredictive control that reflects the diversity observed in empiricaldata-driven models can aid in quantifying the end-to-endgeneration-to-load system benefits of automatic residential load shapingand modulation. While studying the foregoing and examining load add andshed curves as a function of time of day for the MPC-based control ofair-conditioning, the following sub-hypothesis was also developed: TheMPC of distributed energy resources can be complementary in supportingthe grid at different times of the day. While analyzing load add andshed for RBSA appliances, an early morning state synchronization wasobserved across electric domestic hot water (DHW) heaters. As DHWheaters cycled on, the ability to shed load increased. After heating, ashot water tank temperatures declined, the ability to add load increased.In addition, when analyzing cycling behavior of air-conditioning in thecontext of MPC, opportunities to shed load increased in the afternoon,prompting the hypothesis of complementary behavior among loads. Thishypothesis and sub-hypothesis were motivated by the possibility ofmodeling complementary flexibility among multiple degrees of control.Further motivation was the possibility to provide insight to improve a)efficiency of generation unit commitment and economic dispatch, and b)appliance designs so that they might provide greater flexibility by, forexample, DHW heaters and refrigerators incorporating phase changematerials or greater thermal mass.

3.2.3 Hypothesis 3: Combining models through co-simulation can aid inestimating the value of ARLS. Combining the MPC of distributed energyresources with production cost models, through co-simulation, can aid inestimating temporal value across a range of climate zones and geographicareas. To the best of the author's knowledge, this co-simulation had notbeen accomplished by others, and could possibly inform the economicjustification of demand flexibility. The basic premise to be exploredwas: Could a residential load model be combined with a production costmodel in order to determine variable generation costs and CO2 emissionsfor different MPC cases and RES penetration scenarios? This hypothesiswas developed to further the work in 1994-1995 to superimpose timeseries curves of generation supply and user demand from the Platte RiverPower Authority. Overlaying capacities of generation supply, e.g., X MWof nuclear+Y MW of coal+Z MW of natural gas, against the rising andfalling user demand, exposed many periods when marginal generationoutput was low or nil, and hence very expensive on a per unit (e.g.,MWh) basis. Motivation to explore this hypothesis came from recentavailability of building, distribution, and production cost modelingtools.

3.3 Outline of Remainder of Invention

The three-phase research approach conducted in this invention includedPhase 1, Quantifying and preserving, as necessary, the observedinstantaneous load add and shed diversity in empirical applianceelectricity usage data. Phase 2, Developing physical models andMPC-based simulations that aggregated homes while reflecting thediversity in energy usage observed in the empirical data, particularlyelectric DHW heater usage data. Phase 3, Estimating the impact of ARLSon variable generation costs and carbon dioxide emissions. The goals inPhase 1 were to apply statistical methods to quantify the diversityobserved in real-world empirical appliance measurements at varyingspatiotemporal scales in order to inform simulation. The experiments inPhase 1 were chosen to capture the energy usage diversity related tounknowns that would be costly or impractical to ascertain on a massscale such as building size and construction, varying numbers ofbuilding occupants, occupant behaviors, and age of appliances. As theyare significant drivers of residential load, the energy usage statisticsfor electric DHW heaters were used to inform the fidelity of the modelsdeveloped in Phase 2, specifically around the timing of energy usage byDHW heaters. Chapter 4 completed the Phase 1 goals.

Phase 2 were to develop physical models that reflect the energy usagediversity observed in Phase 1, e.g., for the DHW heater, and then applythese models in the context of MPC to calculate instantaneous load addand shed opportunities at the electrical feeder level across all U.S.climate regions for a hot summer day. Phase 2 involved working withGridLAB-D, GridMPC, and creating physical models and simulations toestimate flexibility in electrical demand provided by the MPC ofair-conditioning, battery storage, and electric DHW heating. Thenationwide study in Chapter 5 completed the part of Phase 2 dealing withthe MPC of air-conditioning and includes pricing-based control of anelectrical distribution feeder. In order to estimate the value of ARLS,the flexibility models developed in Phase 2 were explored in the contextof unit commitment of the Texas fleet of 263 thermal generators andnearly 20 GW of wind and solar RES.

The goals in Phase 3 were to: 1) Create realistic models of utilitygeneration, distributed generation, distribution grids, and load acrossthe state of Texas. 2) Jointly optimize supply and demand by calculatingand broadcasting optimum load shapes to appliances managed by MPC. 3)Calculate the maximum possible impact in variable generation costs andCO2 emissions and the subset thereof (if any) attributable to ARLS.Chapter 6 completed Phase 2 and Phase 3 goals. Chapter 7 completes thisinvention and is a discussion that includes suggestions for additionalresearch.

Chapter 4 Data-Driven Techniques that Quantify the Opportunity Limits ofAutomatic Residential Electric Load Shaping

4.1 Introduction

To provide insights into residential electricity consumption, thischapter begins by quantifying distributions of observed empirical energyusage over time for 101 homes and the appliances therein. Insightsinclude times and durations of energy use along with reasonable rangesof power, in kW, and energy, in kWh, that were helpful when checking forreasonable behavior of modeled loads in Phases 2 and 3. Visualizationsand numerical summaries of electricity usage are included for differenttypes of appliances by hour, day, and year and provide a sense of theupper and lower limits of individual appliance-level contributions toload shaping. To quantify, visualize, and simulate diversity ofelectricity use across appliances and homes, results from traditionalstochastic measures and univariate autoregressive techniques werecompared with results from spectral methods. To overcome the limitationsof traditional stochastic methods in quantifying diverse, non-Gaussian,non-stationary distributions of observed appliance behavior, recentdevelopments in wavelet-based analysis were applied to capturetime-frequency domain behavior. To overcome limitations in visualizingdiverse energy usage using boxplots, heat maps, and spectrograms, awavelet-based plot of time-frequency was applied. To overcomelimitations in simulating diversity using traditional autoregressivetechniques, a wavelet-based autoregressive method was applied, andperformance characterizations were made.

In recent DR research, progress has been made in evaluatinginstantaneous opportunities to add and shed residential electric load.Residential DR programs are typically implemented as infrequent,utility-initiated, short-duration deferrals of peak demand throughdirect load control where customers allow their utility to remotely turnoff appliances such as air-conditioning and water heating a few times ayear for a credit on their electric bill. Despite the promise of loadmanagement through supervisory control of the Internet of Things (IoT),direct load control has remained the primary form of residential DR forseveral decades. However, direct load control was never designed to addand shed load to accommodate the ebb and flow of wind and solar energy.As an alternative to direct load control, in this chapter, automaticresidential load shaping (ARLS) is explored as a load elasticitysolution for maximizing the system-wide efficiency of electric powergeneration via intraday control of IoT devices while meeting the needsand comfort preferences of consumers.

To minimize consumers' cost of electricity, an increasing number ofsmart homes with IOT devices can transition from autonomous toorchestrated operation that shapes load to favor energy from lower-costwind and solar generation and higher efficiency conventional generation.Today, loads are typically created by controllers that are based onfixed temperature or battery charging setpoints; as such, these loadsare considered inelastic in time. In the future, new Internet connectedloads such as heating, ventilation and air-conditioning (HVAC) systems,refrigerators, freezers, domestic hot water (DHW) heaters, and batteriescould receive forecast dynamic pricing of electricity or other loadshaping signals that introduce elasticity by allowing each to choosemonetarily or environmentally advantageous times to add or shed load.For example, changes in pricing could be used to update setpoints,allowing IoT devices to continually implement least cost operatingstrategies. In doing so, instead of electrical supply meeting demand,load shaping would become increasingly important in encouraging elasticdemand to enable the cheapest sources and times of supply, therebyreducing thermal and greenhouse gas emissions from power plants whilemaximizing the usage of clean energy from renewable energy sources(RES).

Understanding the limits of load add and shed opportunities would informthe design of generation, transmission, buildings, and appliances insupport of joint optimization of power production and electric load. Forexample, this may support the business case for hot water heaters,refrigerators, and freezers to have increased thermal storage in orderto maximize usage of wind and solar energy. Modeling diverse energyusage in residential loads can be problematic due to different modelsand ages of appliances. Furthermore, residential loads often exhibitnon-stationary energy usage behavior based on the unknown needs ofoccupants that may vary by hour of the day, day of the week, seasons,holidays, shopping schedules, home cleaning schedules, and vacations.Non-stationary energy usage is difficult to quantify and simulate usingtraditional stochastic methods. Preserving energy usage diversity canraise the fidelity of electric load models, allowing for more realisticsimulation of the generation-to-load system-level response to pricingsignals intended to shape residential demand. The role of system-levelresponse gains importance in the application of increasing penetrationof wind and solar renewable energy sources (RES). Despite agingcomponents and ever-increasing complexity, the evolving electric grid ishighly reliable though expensive to operate. In order to accommodatespatiotemporal changes in inelastic load along with variable anduncertain generation from renewable energy sources (RES), expensivemarginal generation and reserve capacity are kept online and dispatchedas needed. To address environmental concerns and reduce the cost ofgeneration, RES are becoming more prevalent with an increasing number ofcities, counties, states and nations aspiring to high RES penetrations,some as high as 100% by 2030. Because RES are less forecastable and someare not dispatchable at all, there is a growing need for creating loadelasticity that can accommodate increasingly volatile supply-demandmismatches.

This chapter extends the investigations of the opportunity limits ofARLS by quantifying load shaping opportunities and uncertainty across avarying number of homes and applying recent developments in spectralsimulation techniques from hydrology research. The spectral techniquesare applied to solve the research question of quantifying and simulatinginstantaneous load shaping opportunities based on empirical data thatreflect non-stationary appliance energy usage. The novelty of this workis the evaluation of empirical in-home measurements as seeds for thecreation and scaling of realistically diverse appliance demand profiles.Simulation of diversity in energy consumption without a priori knowledgeof specific appliance and usage characteristics is significant as itprovides building blocks for mimicking energy usage behavior in asubdivision of homes for DR planning and operational decision making.Section 4.2 presents an additional literature review on residential DR.Section 4.3 describes the methodology. Section 4.4 discusses results,and Section 4.5 presents conclusions and outlook for future work.

4.2 Domain-Specific Literature Review

Research in residential DR was reviewed with the goal of identifying:(1) State-of-the-art, system-level price response approaches involvingtime-elastic end uses, (2) Price-response modeling gaps, (3)Price-response human behavioral issues, and (4) Recommendations forfuture price-response research. There was an overall scarcity ofsystem-level price-response models and a plethora of subsystem modelswith limited or unspecified spatiotemporal resolutions. Darby andMcKenna suggested that new DR measures will be needed to shape loadthroughout the day. Likewise, based on recent experience in UnitedStates and Europe, the significantly less predictable and more volatilenet load after renewable generation (i.e., total load less thegeneration from RES) will need to be smoothed by DR. Results ofelasticity experiments by McKenna and Keane found the introduction ofdynamic pricing reduced diversity of demand and increased coincidentalresponse by promoting the same characteristics of response among(Internet-connected) automated appliances.

A review of 117 residential electricity demand models indicatedsignificant variability across households and raised questions as towhether high-resolution stochastic modeling approaches provide anadequate representation of the real-world load characteristics ofappliances. Adequate representation is important given the massive bodyof model-based time-of-use and real-time pricing assessments that havebeen used to address various aspects of residential DR behavior.Furthermore, coupling the inherent limits of stochastic models alongwith diversity being reduced by pricing-based response further raisesthe concern for adequately modeling appliance behavior. In a study ofthe most comprehensive data set of metered electricity demand in theUnited Kingdom, empirical and simulated consumption data were analyzedon an aggregated annual basis. The comparison used qualitative andquantitative methods between simulated and metered data sets, anddiscrepancies were found in overall household and individual applianceselectricity consumption, where non-normality of the data was apparent.

A kernel density estimate of the distribution of empirical annualconsumption data revealed the existence of a trimodal underlyingdistribution, which makes intuitive sense at both the appliance andhousehold level. For example, around the world, electric hot waterheaters are 1) most often in standby mode drawing no power, 2) are lessoften in short recharge mode when recovering from standby losses orlight usage activities such as washing hands, or 3) are in long rechargemode when recovering from high-usage activities such as dish and clotheswashing. A different study, aggregating large numbers of residentialappliances for DR applications, used a methodology based on amulti-class queuing system, where each class represented demand blocksof a specific power level, time duration, and a service delayrequirement. The model minimized the cost of the appliances aggregatedpower consumption under day-ahead pricing. A shortcoming of the modelwas the randomization of demand data from a single consumer to representthe demand behavior of 1,000 consumers. Overall, review of theliterature suggested that further empirical, bottom-up, end-to-endsystem models are lacking and needed to simulate and optimize the impactof DR on maximizing the efficient usage of RES and thermal generation,along with top-down policy measures that provide appropriate incentives.

4.3 Methodology

4.3.1 Data and Methods

All data in this study came from the Northwest Energy EfficiencyAlliance, Residential Building Stock Analysis (NEEA RBSA): MeteringStudy, based on field data from a representative random sample ofexisting homes in WA, OR, ID and Western MT in the Northwest of theUnited States. The NEEA RBSA encompassed 29 months of energy usage in15-minute observations of single-family homes and data readings wereavailable for 90.5% of the intervals over this period. Observationsincluded total per residence electricity usage at the service entrancealong with up to 25 individually measured loads per home that wereacquired and reported separately, including various types of HVACsystems, appliances, lighting, entertainment, home office, and plugloads. The first of two NEEA RBSA reports contained attributes of 1,400single-family homes. In addition to building age, envelope dimensions,insulation values, etc., a cross section of vintage and type ofappliances were available though not included in this study. The secondNEEA RBSA report covered a subset of 101 homes and loads therein, whichwere the data used in this study. In particular, the thermostaticallycontrolled load (TCL) appliance data revealed how each device couldprovide ARLS capability. The TCL energy usage per interval allowed forthe creation of detailed load shapes that provided insights to thevariability in whole-house load.

The NEEA RBSA data captured diversity in energy usage among homes andappliances likely due to occupancy patterns, hour of day, day of week,seasons, holidays, shopping and home cleaning cycles, vacations thoughnone of these parameters are in the dataset. A continuum of short tolong appliance run times were evident, reflecting the possibility thatsickly or high-use appliances, some which operated nearly continuously,would not be able to participate in ARLS. Vigilance around data accuracywas critical during extraction, transformation, and loading ofobservations. Some data were missing time stamps, some were out of range(positive and negative), and others were missing. Data anomalies broughtinto question potential gaps or errors in acquisition, along with thepossibility that some appliances, such as a secondary refrigerator orfreezer, were intentionally turned off for days, weeks, or months.Energy units of kWh/15-min are referenced in this study due theunavailability of instantaneous power measurements.

FIG. 2 shows when an appliance was operating, particularly energy usageof TCL appliances on July 3-4, over a year, showing kWh per 15-minuteinterval. Individual bar width is 15 minutes, and the height of each bardenotes the kilowatt-hours of energy used in that 15 minutes. A largecolored region indicates a long run time for example, a refrigeratorcooling down after being refilled with groceries. House numbers appearafter appliance names and vertical dashed lines separate days. Note thediversity in energy usage along axes: (a) two refrigerators, the one atright with a long run times in evenings and higher peak use; (b) twofreezers, the one at right with nearly symmetric run times and lowerpeak use; and (c) two DHW heaters with typically low run times, the oneat right with consistently higher peak usage.

Distributional statistics for NEEA RBSA TCL appliances were calculatedand visualized using stochastic and spectral methods. Next, a binaryconditional operational model was developed to accommodate appliancediversity in start time, frequency of use, duration of use, and energyconsumption. Lastly, empirical data were simulated, and the probabilitydensity functions (PDFs) of resulting ensembles of simulations werecompared to observations. 4.3.2 Modeling TCL Behavior Using NEEA RBSAData To capture the energy usage diversity in the NEEA RBSA data set,each TCL appliance was viewed as a contributor to a desired loadincrease or decrease based upon its on or off state in time. Loadshaping opportunities were estimated throughout the day wherein TCLappliances were assumed to have Internet connectivity and the ability tochange setpoints automatically to execute financially beneficial on andoff choices during periods of low and high energy costs. An extremeillustrative case assumed contiguous non-overlapping temperature controlsetpoints for a DHW heater, as shown in Table 1, wherein the on or offstate of the appliance was used to calculate the load increase ordecrease opportunity at any point in time given an electricity pricechange. To simplify calculation of the potential for load shaping, itwas further assumed that TCLs always operated within their controldifferential dead band.

TABLE 1 Sample DHW heater non-overlapping setpoints. The ‘Not modeled’entries reflect model constraints that limited operation between 120 and130 F. inclusive. Temp. F. High $/kWh Low $/kWh 131 and above Notmodeled Not modeled 130 Always OFF Turn Off 129 Always OFF Stay ON 128Always OFF Stay ON 127 Always OFF Stay ON 126 Always OFF Stay ON 125Turn OFF Turn ON 124 Stay ON Always OFF 123 Stay ON Always OFF 122 StayON Always OFF 121 Stay ON Always OFF 120 Turn ON Always OFF 119 andbelow Not modeled Not modeled

Whenever the price of electricity changed, from high to low, or low tohigh, TCL appliances reacted as described in Table 1. This logic wasapplied to TCL appliances to create a time series of Load Add and LoadShed opportunities which were summed for a single house or group ofhouses, without regard for phenomena such as the inefficiency ofpreheating and the impacts of energy rebound. Ideally, load add and shedwould be expressed in units of power (kW). That said, only units ofenergy (kWh) were available in the RBSA Metering study. At any point intime, an appliance was either on or off. Looking ahead over n time stepsat an individual appliances energy use over time, a maximum load, Lmax,was determined. Likewise, at any time, t, the above logic was evaluatedto calculate the load add or shed opportunity, OP. Given a high price ofelectricity, if an appliance was off, it was incentivized to turn onwith a low price of electricity, and the turning on resulted in a loadaddition, Ladd, equal to Lmax, as in equation 4.1.

L _(add) ^(appliance) =OP _(add load) ^(OFF appliance) =L _(max(t,l+n))^(appliance)  (4.1)

In this model, if a partial load was present, then no load addition wasapplied, even though Lt may have been less than Lmax.

Given a low price of electricity, if an appliance was on with a currentload, Lt, it was incentivized to turn off with a high price ofelectricity, and the turning off resulted in a load shedding, as inequation 4.2:

L _(shed) ^(appliance) =OP _(shed load) ^(ON appliance) =−L _(t)^(appliance)  (4.2)

Summing among TCL appliances in a specific home yielded the upper andlower limits of aggregate load that could be added or shed as inequations 4.3 and 4.4:

$\begin{matrix}{L_{add}^{home} = {\sum\limits_{TCLappliances}L_{add}^{appliance}}} & (4.3) \\{L_{shed}^{home} = {\sum\limits_{TCLappliances}L_{shed}^{appliance}}} & (4.4)\end{matrix}$

Summing among a group of homes yielded an aggregate load that could beadded or shed as in equation 4.5 and 4.6:

$\begin{matrix}{L_{add}^{homes} = {\sum\limits_{homes}L_{add}^{home}}} & (4.5) \\{L_{shed}^{homes} = {\sum\limits_{homes}L_{shed}^{home}}} & (4.6)\end{matrix}$

To simplify the above, the concept of a duty cycle was used to summarizethe on and off behavior of a TCL appliance over time. Duty cycle, DC,described the behavior of a device that operated intermittently ratherthan continuously; it was the fraction of time a device was on dividedby the total time, as in equation 4.7:

DC_(l,l+n)=(ON time)_(t,t+n)/(total time)_(t,t+n)  (4.7)

Over time, an appliance with a low duty cycle typically had a lowopportunity to shed load as it was most likely already off. Likewise,somewhat counter-intuitively, a low duty cycle indicated a highopportunity to add load, albeit for perhaps only a short duration.Conversely, an appliance with a high duty cycle typically had a highopportunity to shed load and a low opportunity to add load, as inequations 4.8 and 4.9:

OP _(t,t+n) ^(appliance add load)=1−DC_(t,t+n) ^(appliance)  (4.8)

OP _(t,t+n) ^(appliance shed load)=DC_(t,t+n) ^(appliance)  (4.9)

The opportunity to add and shed load was summed among TCL appliances andhomes as in equations 4.3, 4.4, 4.5, and 4.6 to yield the instantaneousaggregate upward and downward load-shaping opportunities. It iscritically important to note that following an instantaneous loadincrease or decrease event, the future operation of a TCL appliance maybe constrained, e.g., due to comfort constraints, and load add or shedcannot be controlled continuously. Out of scope of this chapter, thoughanalyzed in following chapters, are the length, periodicity andresulting load add and shed opportunities after appliances participatein a load increase or decrease event.

4.3.3 Scaling Up the NEEA RBSA Dataset

Diverse profiles from thousands of homes are required for futureapplications of this work involving the joint optimization of generationand load. In simulating ensembles of synthetic appliance data, spectraldecomposition and reconstruction were used to preserve the observeddiversity in energy use. Spectral methods captured the non-normal,non-stationary energy usage of appliances and met the goal of specifyingmore realistic probability distribution functions than stochasticmethods.

Traditional stochastic methods that were crafted to capture measuressuch as mean, variance, and skew can fail to reproduce significantspectral properties of the observed data. This failure to reproducespectral properties can lead to an inaccurate estimation of load. Assuch, three variants of the wavelet auto-regressive method (WARM) werecompared in their ability to capture and recreate appliance behaviorinvolving the hour of day, the day of week, shopping cycles, the timingof house chores, seasonal weather patterns, family vacations, andvarying numbers of occupants.

As a first step, the TCL appliance data was decomposed via continuouswavelet transform. Wavelets may be localized in both time and frequencywhereas the standard Fourier transform is only localized in frequency.Components were identified based on the peaks in the global(time-averaged) wavelet spectrum. The approach decomposed a time seriesinto various components at several frequencies via the wavelettransform; this provided the power (or variance) of the original data inboth the frequency and time domains.

For a time-series, xt, the continuous wavelet transform was defined asequation 4.10:

$\begin{matrix}{{X\left( {a,b} \right)} = {a^{1/2}{\int_{- \infty}^{\infty}{x_{t}{\phi^{*}\left( \frac{t - b}{a} \right)}{dt}}}}} & (4.10)\end{matrix}$

where a was a scale parameter (2*dt=30 minutes), φ* was the waveletfunction and b was the shift parameter (1*dt=15 minutes). The * denotesa complex conjugate. The Morlet wavelet was a reasonable first choice inwavelet analysis, was most often applied by others with success, and wasgiven by equation 4.11:

$\begin{matrix}{{\phi(\eta)} = {\pi^{{- 1}/4}\exp\;\left( {i\;\omega_{0}\eta} \right)\exp\;\left( {- \frac{n^{2}}{2}} \right)}} & (4.11)\end{matrix}$

where ω0 and η were nondimensional frequency and time parameters,respectively.

The shifted and dilated form of the mother wavelet was given bysubstituting (t−b)/a for η in equation 4.11. For a variety of waveletscales, equation 4.10 can be thought of as a series of convolutionsbetween the wavelet function 4.11 and the original time series at allpoints. The process was simplified as all convolutions were completedsimultaneously at a given scale by the convolution theorem. By doing so,the wavelet transform was defined as the inverse Fourier transform ofthe product of the wave function in the Fourier space and the data.

The wavelet spectrum at different frequencies over time was depicted bya contour plot of the wavelet transform with a companion plot of theglobal spectrum that showed the average variance strength at eachfrequency. Lastly, to simulate the data, phase randomization, a recentdevelopment in wavelet-based simulation methods, was applied andcompared to the auto-regressive and autoregressive integrated movingaverage (ARIMA) simulations of the wavelet decomposed energy usage of aDHW heater over the same hour of a day for an entire year. In an effortto fit the data as well as possible, the phase randomization methodapplied a cosine perturbation to the spectral fit to create an ensembleof DHW heater energy use. Alternative curve fitting techniques weretried and performance compared. A simple auto-regressive process wasapplied to determine if energy usage could be successfully regressed onits own lagged (i.e., prior) values. In an attempt to improve theauto-regressive fit to the observed energy use, the ARIMA process addeda differencing step to accommodate non-stationarity and a linearcombination of error terms for values that occurred contemporaneouslyand at various times in the past.

4.4 Results

4.4.1 Residential Appliance Load Profiles

Stochastic analysis of empirical data revealed diverse, non-normaldistributions of energy usage for the studied TCL appliances. Inaddition, non-stationary usage was indicated by a nonconstant mean andvariance in different time epochs. The empirical 15-minute observationswere dominated by zero values and had long tail frequency distributions.Once zero values were removed, kernel density estimates providedinsights to bimodal distributions of air conditioner and refrigeratorbehavior and trimodal distributions of freezer and hot water heaterbehavior. Lastly, spectral methods provided both visualizations ofdiverse and non-stationary energy usage as well as PDF ensembles ofsimulated hot water heater behavior. The observed energy usage ofappliances varied by a factor of 2 or more, which assumed continualusage on an annual basis. As expected, all homes had a primaryrefrigerator. About a quarter of homes had a secondary refrigerator, andalmost 40% of homes had a stand-alone freezer. A total of six homes hada secondary freezer and the low the number of samples for this appliancetype indicate there were many NAs in the data, indicating missingobservations, perhaps because secondary freezers were not operatedyear-round.

The diversity in empirical energy consumption impacted the bounds ofenergy usage for small sets of homes that are typically fed by asplit-phase transformer. For example, depending on the number of homes,the mean energy used to heat hot water had wider bounds with fewer homessampled. Looking at electric energy usage for heating DHW over theinterval 00:00 to 00:15 on Apr. 1, 2012 it is observed that there is anuncertainty in adding or shedding load as a function of the number ofparticipating houses. Simply put, an increase in participating homesresulted in greater certainty in the amount of load that could be addedor shed.

Focusing on a single DHW heater, the distributional statistics ofelectric DHW heater energy usage varied per 15-minute interval and perday were observed and is representative of observations of electric DHWheaters in other homes. It was found that the spread in statisticsprovided insight into the diversity in the energy usage of a singleappliance, in this case, a DHW heater. Note the daily sum varied by afactor of approximately eight. Summing DHW heater energy usage into1-hour intervals, an annual distribution of usage by the hour of the daywas determined.

Electric DHW heater energy usage in another home per hour of dayrevealed more outliers but lower interquartile variance in early morninghours. It was inferred from the usage chart that 5 AM is the start ofincreased hot water usage in the morning and is among the high-varianceoff-peak hours. Hours of high variance can result in difficulties inestimating instantaneous load add and shed opportunities. As such, the 5AM hour was chosen as a difficult test case for evaluating curve fittingand creating simulation ensembles. If 5 AM daily energy usage could besimulated for one DHW heater, other hours, water heaters, homes andcities could be modeled similarly.

The limitations of conventional linear and quadratic curve fittingmethods were evident when attempting to capture the energy usagevariance and resulted in unsatisfactory curve fits to the time-varying,non-stationary empirical appliance usage data. As a solution test case,the spectral WARM method was applied to decompose and reconstruct theenergy usage of DHW heating in the 5 AM hour over the course of a yearand resulted in a nearly perfect curve fit as shown in FIG. 3 (sixmonths are shown for visual clarity of chart).

FIG. 3 shows a wavelet decomposition and aggregation in the enhancedWARM-based curve fit of 5 AM hourly energy usage of DHW heater in RBSAhome 10388 from Q2-Q3 over a year inclusive. Prediction errors in the ONstate are depicted by vertical offset between the observed value at topof each bar and its corresponding wavelet reconstructed value denoted asa dot; errors in the OFF states include non-zero values viewed along theday-axis.

4.4.2 Residential Load Shaping Opportunities

Diversity in appliance empirical energy usage resulted in varying loadshaping opportunities across the studied NEEA RBSA homes, of which, 57homes used electricity to heat DHW and 44 used gas. To estimateopportunities for each 15-minute interval, (1) and (2) were evaluated tocalculate the ability of each individual electric TCL appliance to addand shed load using a look-ahead interval of 24-hours for Lmax.Likewise, for each specific home, results were summed among TCLappliances using (3) and (4) to calculate the upper and lowerinstantaneous limits of load shaping, as shown in FIG. 4. (six-hours arechosen for visual clarity of chart) and Table 4.2.

FIG. 4 shows the energy usage profile of RBSA home 13019 at 15-minuteintervals. The hatched line labelled service is the whole-buildingelectric service, the portion leading up to the hashed dotted linelabeled Increase is the instantaneous load that could be added, and theportion descending to the solid line labelled Decrease is theinstantaneous load that could be shed. Energy usage of individual TCLappliances in the home appear in hashed lines labeled Refrig, Refrig_2,and Freezer at the bottom of the graph. RBSA home 13019 isrepresentative of homes with gas DHW heaters.

Table 4.2 tabulates load-shaping opportunities for Home 13019 based on15-Minute intervals during first six hours.

TABLE 4.2 Opportunity Max Min Mean Increased load [kW] 0.800 0.360 0.587Decreased load [kW] 0.636 0.302 0.442

To evaluate instantaneous load shaping opportunities among groups ofhomes, results from individual homes were summed using equation 5 and 6.Summing whole-building electric service, as well as the upper and lowerlimits among the 14 NEEA RBSA homes exhibiting best data quality,yielded an aggregate load that may be added or shed at any point intime, as shown in FIG. 5 (14 homes are chosen for visual clarity ofchart).

FIG. 5 shows the aggregate load profile of 14 RBSA homes at 15-minuteintervals. The black line labeled Service is the home electric use, theportion leading up to the hashed line labeled Increase is the possibleinstantaneous load that could be added, and the portion descending tothe hashed line labeled Decrease is the possible instantaneous load thatcould be shed. The red spikes indicate opportunities to add load, forexample, following completion of DHW heating resulting from earlymorning widespread synchronized use of hot water. Mid-day and eveningload shaping opportunities were also evident.

Summing across multiple houses showed that significantly more load couldbe added than shed at any point in time. This is mostly attributable toa DHW heaters low duty cycle and high instantaneous load, which is onthe order of 10 to 40 times greater than that of refrigerators andfreezers.

4.4.3 Visualization of Appliance Loads

The results discussed thus far have not provided visual insight toappliance energy usage that varies over time. While results haveindicated temporal diversities, they lack numerical summaries thatquantify behavior. Furthermore, using one pixel on the time axis todenote 15-minutes, the number of pixels required becomes unwieldy whenattempting to visualize long periods of a year or more. As analternative, a visual sense of the mean, median, interquartile range,outliers, and positive skew all of which quantify behavior over time,lack the ability to depict behavior changes between intervals.Similarly, other results lack the ability to depict inter-intervalbehavior, e.g., from any single 15-min to another. In summary, while asense of distributions of energy use over a period and provide insightsto the normality of the data can be obtained, they do not provide asense of behavior at specific points in time.

Heat maps can be helpful in viewing energy usage over multipleintervals. An energy use heat map displays time on both axes, e.g.,individual days on the horizontal axis and individual 15-minuteintervals on the vertical axis. As depicted near the center of FIG. 6,Day 4 had several periods of high energy use.

Another heat map may show energy usage of DHW heater in RBSA home 2284over the first 7 days of 2Q. Colored bars depict electricity use in15-minute intervals and 1.0 or above denotes high use. Note several highenergy use periods, particularly on Day 4 before 12 noon. In a heat map,the number of time intervals on the horizontal axis may be increased inorder to view more days, for example electricity use over 30 days.

Another such heat map may show energy use of DHW heater in RBSA home2284 over the first 30 days of 2Q. Colored bars depict electricity usein 15-minute intervals and 1.0 denotes high use. Note several highenergy use periods, particularly on Day 4, 11, 12, 15, 23, and 24. Inaddition to high electricity use on Day 4, other high use periods areevident. Heat maps become increasingly difficult to read in the presenceof non-stationary behavior, e.g., the red regions in 4.11 denote highelectricity usage occurring at different times on the day. Whenattempting to visualize behavior over very long periods, heat maps havepixel limitations similar to bar plots. The visual information in ayear-long heat map can be blurred by nonstationary behavior.

Another heat map may show energy usage of DHW heater in RBSA home 2284from 2Q of Year 1-1Q of Year 3 inclusive. Colored bars depictelectricity use in 15-minute intervals and red denotes high use. Notethe faint thin white horizontal band denoting nearly consistent energyuse at 5 AM on most days. Also note the non-stationary high energy useintervals in the late morning, afternoon, and evening on most days. Highelectricity use can also be observed at approximately 6 AM on and nearday 600. Spectrograms can be helpful in viewing appliance electricityusage over time. A spectrogram is a visualization of the spectrum offrequencies of a signal as it varies with time. There is much recentliterature on disaggregating household loads by using spectrogramanalysis to discern the time frequency signatures of individualappliances such as kettles, refrigerators, dishwashers, microwave ovens,washing machines, and televisions. In addition, spectrogramvisualization may be applied to a specific appliance, in this case, aDHW heater. A spectrogram may be created using a 1-day window of 96samples to depict the frequency of energy use by the electric DHW heaterin RBSA home 2284 over 30 days.

Such a spectrogram of DHW heater energy use in RBSA home 2284 over thefirst 30 days of 2Q. An oscillogram may be plotted beneath thespectrogram and denotes peak energy use. High energy use periods on days11, 12, 15, 23, 24, and 29 were observed. The size and shape of aspectrogram analysis window can be varied. A shorter (smaller) windowproduces more accurate results in timing at the expense of precision inrepresenting frequency. A longer (larger) window provides a more preciserepresentation of frequency at the expense of precision in representingtiming. The daily window size presents challenges when depicting a verylarge number of days.

Another spectrogram may show usage of DHW heater energy use in RBSA home2284 from 2Q of Year 1-10 of Year 3 inclusive. An oscillogram is plottedbeneath the spectrogram may denote peak energy use. Only a few detailsare discernible such as lower energy use in the first 200 days andhigher energy use just before and in the period after Day 600. Theinclusion of 2 years of daily spectrogram windows showed only a fewunique details being discernible such as lower energy use at left andhigher energy use.

Wavelet analysis is becoming a common method for analyzing, visualizing,and simulating localized variations of power within a time series. Amajor benefit of wavelet visualizations is their ability to convey morecomprehensive information than traditional distributional metrics andvisualizations such as boxplots and histograms. For example, the waveletvisualization for a single DHW heater discussed above may be based on 25months of 15-minute intervals.

4.4.4 Simulation of Appliance Loads

Having discussed methods and results for quantification andvisualization of appliance energy usage, this section presents andcompares simulation via several methods. Using a nonparametric densityestimation technique, spectral reconstruction was used to simulate PDFensembles of the 5 AM energy usage of a DHW heater, which were comparedto the PDF of the empirical data. There were differing results from thesimulations based on wavelet-based phase randomization, straightautoregressive, and ARIMA methods. The phase randomization methodapplied a cosine perturbation to the spectral fit and did the best jobcreating ensembles of DHW heaters that model the empirical PDF, as shownin FIG. 7.

A similar simulation of the wavelet may be constructed that isdecomposed 5 AM hourly energy usage by DHW heater in RBSA home 13088from Q2 Year 1-Q1 Year 2 inclusive, using the phase randomizationmethod. The straight autoregressive and ARIMA simulation results wereobtained using the stats::arima.sim function from the R programmingenvironment. The simulations based on the straight autoregressive methodperformed similarly to ARIMA simulations, with PDF ensembles from bothmethods showing poor fits.

Another simulation of the wavelet decomposed 5 AM hourly energy usage byDHW heater in RBSA home 13088 from Q2 Year 1-Q1 Year 2 inclusive, usingthe autoregressive ARIMA method. In both simulations ensembles are notclose to the empirical PDF. Also, note the high occurrence ofunrealistic negative values further indicating poor curve fits by thestraight autoregressive and ARIMA simulation methods. The phaserandomization method most accurately modeling the observed behavior ofthe empirical PDF was explored. Then comparison of phase randomizationand ARIMA simulation techniques of the wavelet decomposed 5 AM hourlyenergy usage by DHW heater in RBSA home 13088 from Q2 Year 1-Q1 Year 2inclusive was observed.

To quantify the performance of the simulation methods, distributionalstatistics for the first, second, third and fourth statistical moments(mean, variance, skew and kurtosis) were shown for all simulations,along with maximum, minimum, and sum. For comparison, the performance ofeach simulation method was shown along with statistics from theempirical observations. For most statistical measures, the phaserandomization method had better simulation performance than either thestraight autoregressive or ARIMA methods.

Mean and variance comparing the performance of reconstruction methods insimulating 5 AM hourly energy usage by the electric DHW heater in RBSAhome 13088, from Q2 Year 1-Q1 Year 2 inclusive. Statistics of empiricalobservations are denoted by red dots. For mean and variance, phaserandomization provided superior performance. An unrealistic slightlynegative mean energy usage and spread in variance in both the straightautoregressive and ARIMA simulation methods was observed.

Skew and kurtosis were plotted comparing the performance ofreconstruction methods in simulating 5 AM hourly energy usage by theelectric DHW heater in RBSA home 13088, from Q2 Year 1-Q1 Year 2inclusive. Statistics of empirical observations are denoted by red dots.For skew and kurtosis, the phase randomization method had somewhatbetter performance. The statistics of all simulation methods were lessthan in the observed RBSA data.

Maximum, minimum, and sum comparing the performance of reconstructionmethods in simulating 5 AM hourly energy usage by the electric DHWheater in RBSA home 13088 were obtained, from Q2 Year 1-Q1 Year 2inclusive. Statistics of empirical observations are denoted by red dots.Note: (a) the significant variances in the maximum statistic wouldadversely affect load shaping calculations, (b) the minimum statisticincluded unrealistic negative values, and (c) Mean values of zero in theAR and ARIMA sum statistics were unrealistic. This further highlightsthe challenges in simulating RBSA appliance usage data, in this case,for a single DHW heater. Note that all simulation methods understatedboth peak usage and minimum usage, some more so than others. Analyzingthese simulations highlighted limitations in all simulation methods andquantified the superior performance of phase randomization over both thestraight autoregressive and ARIMA simulation methods.

In summary, results indicate the abilities of different types ofInternet-connected appliances to add and shed electric load throughoutthe day. The implications of automatically adding and shedding loads aresignificant in the context of the grid supporting increased penetrationof RES. Results also indicate the improved performance of spectralmethods over traditional statistical methods in the ability to quantifyand simulate non-stationary behavior, which addresses concerns in theliterature of preserving energy use diversity and improving modelfidelity for realistic simulation of the generation-to-load system-levelresponse.

4.5 Conclusions and Outlook for Future Work

In this study, it was assumed that utilities would evolve beyond directload control and use ARLS to create elasticity in demand by continuallybroadcasting a forecast dynamic price of electricity to IOT appliancesin order to maximize generation efficiency and minimize the cost ofelectric power production and consumption. Changes in pricing resultedin instantaneous load add and shed opportunities which were quantifiedfor individual and groups of NEEA RBSA single family homes in thePacific Northwest of the United States.

Empirical data were explored, resulting in several interestingstatistics and features, including the relationship between duty cycleand instantaneous opportunities, however brief they might be, to add orshed electric load. Wavelet spectral analysis was applied to capture andview diverse and unknown drivers of load such as the type, age, and timeof use of appliances and occupancy characteristics. The performance ofWARM phase randomization, auto-regressive and ARIMA simulation methodswere compared; the ability of each method to reflect diversity in energyusage of an actual DHW water heater in a high-variance hour over thecourse of a year was quantified, with phase randomization providing themost accurate simulation ensembles.

Most importantly, this work provided insights in quantifying diversityin appliance energy consumption without a priori knowledge of appliancedetails and in simulating load ensembles that reflect observed energyuse. The main contribution is that a robust simulation technique likeWARM provides the ability to simulate synthetic subdivisions for use inenergy management research. The WARM can be used to simulate a varietyof ensembles mimicking each appliance in a subdivision in order toaggregate statistics of energy usage, by house and electricaldistribution feeder, for potential decision making in managing the grid.

The research and results described in this chapter provided insightsinto the characteristics of residential electricity consumption.Insights based on observed empirical energy usage included times anddurations of energy use along with expected ranges of power and energythat were helpful when checking for reasonable behavior of the loadsmodeled in Phases 2 and 3. Visualizations and numerical summaries ofelectricity usage provided a sense of the upper and lower limits ofindividual appliance-level contributions to load shaping. The resultshave been helpful in understanding expected appliance, home, anddistribution feeder behavior with and without ARLS. Of immediate use inthis research was finding a disagreement between the GridMPC simulateddata and the RBSA empirical data regarding the timing of energy usage byDHW heaters. GridLAB-D is the origin of the DHW heater energy useschedules that are implemented in GridMPC simulation. A discrepancy inDHW heater operation in early morning hours motivated usage schedulemodifications during Phase 2 of this research. Additional detail appearin Chapter 6.

Chapter 5

Characterizing Potential Electric Grid System Benefits of MPC-basedResidential Load Shaping

5.1 Introduction

This chapter explores the potential for price-responsive control ofresidential air-conditioning to shape electric demand at thedistribution feeder level in order to minimize electricity productioncosts. First, motivation is provided for flexibility, particularlyflexible building loads. Second, physical models of the interplaybetween building thermal and electric loads are used to simulatetime-series temperature and load behavior. Third, instantaneousload-adding and load-shedding opportunities are quantified in more than100,000 individual homes on 204 distribution feeders with resultspresented for 35 cities across the United States. Fourth, in the contextof distributed model predictive control, simulation of feeder-levelresponse to a residential day-ahead 5-minute pricing vector to 2,146homes highlights an aggregate impact of flexible loads. Buildings aresignificant users of energy, responsible for more than 73% of the totalelectricity usage in the United States, with about 50% of thatconsumption occurring in residential buildings. As such, the ability forbuildings to provide grid-controlled flexible load can be criticallyimportant.

With increasing penetrations of renewable energy sources (RES) andfossil fuels waning in the electricity generation mix flexible loads canhelp accommodate the variable and uncertainty. Flexible loads can beused to maintain the operational balance between generation supply anduser demand in transmission, distribution, and microgrids.

5.2 Recap of Reduced Order Building Model and MPC

To reduce electric bills, support high penetrations of RES, and achievea host of electric grid benefits, model predictive control (MPC) hasbeen applied in thousands of residential buildings to enable optimalsupervisory control of building thermal mass through the manipulation ofcooling temperature setpoints. Setpoint adjustment enables load-addingand load-shedding opportunities because additional cooling energy isstored in the thermal mass when lowered and released when raised. In theabsence of grid-side control elements, such as load tap changers,distribution grid impacts were evaluated from the perspective ofair-conditioning control on a single electric utility distributionfeeder in three U.S. cities for the typical meteorological month ofJuly. The GridMPC in-home controller developed used a receding horizonMPC scheme to minimize an objective function of building electric energyand demand. Given that there are hundreds or thousands of buildings on adistribution feeder, the size of the decision space makes a centralizedsupervisory control optimization intractable. As such, a decentralized,distributed approach was adopted. Therefore, in GridMPC, a population ofresidential buildings was simulated as being connected to a feeder, andeach performed a separate control optimization independent of the otherbuildings.

To improve computational efficiency and provide timely simulations,developed a reduced order building model (ROM) within GridMPC suitablefor determining electric load throughout the United States. The ROMcombines typical meteorological year (TMY) weather data, buildingenvelope data from the U.S. Energy Information Administration,Residential Energy Consumption Survey (RECS), and several componentmodels for appliances and occupancy. The RECS data were randomly sampledacross several characteristics important to residential energy use,including dwelling type, floor area, envelope integrity, heating typeand setpoint, cooling type and setpoint, and hot water usage. The TMYand RECS data are location specific, capturing variations from one cityto another. Using an electrical circuit analogy, all residentialbuildings on a representative electrical distribution feeder wereexpressed as a thermal network of resistive and capacitive elements. Asan example, for each building, the envelope model illustrated in FIG.5.1 consisted of six components that represented, counterclockwise fromthe upper left, the glazing, roof, walls, floor, internal mass, and air.

FIG. 8 depicts a building envelope model expressed as a thermal network.For each of the solar exposed surfaces, total solar insolation wascalculated from the beam, diffuse, and horizontal components. Likewise,the glazing model was a straightforward extension of the opaque surfacemodel that included a solar heat gain coefficient. Shading by overhangsand fins was also calculated for all solar exposed surfaces. Energybalances were formulated around the individual elements shown in FIG. 8to create a system of ordinary differential equations, which werediscretized in time and solved analytically. As an example, for theexterior wall node, the energy balance was expressed as equation 5.1:

$\begin{matrix}{{\sum Q_{\omega\; o}} = {Q_{solwall} + {h_{\omega\; o}{A_{\omega}\left( {T_{o} - T_{\omega\; o}} \right)}} + {\frac{A_{\omega}}{R_{\omega}}\left( {T_{\omega\; i} - T_{\omega\; o}} \right)} + {C_{\omega\; o}\frac{{dT}_{\omega\; o}}{dt}}}} & (5.1)\end{matrix}$

where:

ΣQ_(ω0) is the energy balance at the outside wall node,

Q_(solwall) is the energy gain caused by solar insolation,

h_(wo) is the outdoor film coefficient, and

A_(w) is the wall area.

In addition to ordinary differential equations for the buildingenvelope, other subsystems were modeled in. A central air-conditioningsystem model combined a DX air cooling coil with a constant volume fanand a dual setpoint thermostat that included hysteresis. Internal heatgains from equipment such as appliances and lights were modeled using anominal energy demand, schedule, fuel type, and sensible heat fraction.The schedule value ranged from 0 to 1, representing the fraction of timethat the equipment is on during a given interval. The heat gain fromequipment was the energy consumed times the fraction of energy convertedto heat. Heat gains from occupants were also modeled. In an annualcomparison of heating and cooling loads, the ROM was found to be inagreement with EnergyPlus (BESTEST-EX), SUNREL, DOE-2.1E, andGridLAB-D).

In summary, the ROM of includes a building envelope model for estimatingheating and cooling requirements; equipment models to calculate electricdemand associated with cooling; a thermostat model to control thecooling operation; simplified end-use models (and the heat gains theyproduce) for appliances and electric hot water heaters. Definitions forsome of these models are described in the EnergyPlus EngineeringReference. Other models are largely derived from the ASHRAE HVAC 2Toolkit.

When operating as an Internet-connected smart thermostat, in the contextof MPC, GridMPC adjusted setpoints in increments of 0.25 K, which is atypical precision of residential thermostats. GridMPC assumed each hometo be unoccupied for 10 hours during the day, starting at 08:00±1 hour.The departure time was randomized for each home to capture occupantdiversity and prevent unintended synchronization. The thermostatsetpoint in an occupied home was altered between +0K and −2K, and in anunoccupied home between +3K and −5K. The −2K lower boundary duringoccupied periods recognized that larger temperature swings would likelycause occupant discomfort. To experimentally explore load shaping,GridMPC was extended by adding estimates of instantaneous electricload-adding and load-shedding opportunities at each simulation timestep. This extended model allows for the creation of nationwidequantitative assessments of the impact of residential load shaping andhelps quantify the electric system benefits resulting from the aggregateeffects of residential load shaping. As only real power is considered inthis experiment, the results are aggregated using the R programmingenvironment and the GridLAB-D distribution simulation software isunneeded.

5.3 Simulation Methodology

To simulate the impact of thermal mass-enabled residential load shapingon the distribution network in 5-minute intervals, the following stepsare summarized here and further detailed next: 1) Hundreds ofprototypical electric distribution feeders in cities across the UnitedStates are populated with the attributes of thousands of prototypicalhomes. 2) The ROM uses one Summer day of TMY weather data to estimatethe whole-building electric demand for each residence. 3) Using theextended model, individual home instantaneous electricload-adding/load-shedding opportunities are calculated on a 5-minutetimescale based on differences between air-conditioning thermostatsetpoints and zone temperatures. 4) Each home's electric loads andinstantaneous add/shed opportunities are aggregated to the feeder level.5) Feeder loads and instantaneous add/shed opportunities are aggregatedto the city level. 6) As a separate activity, GridMPC uses 5-minuteday-ahead forecast pricing to control air-conditioning load, in thecontext of distributed MPC, to simulate a single feeder-level responseto residential load shaping.

Step 1) Using data from the RECS, the MATLAB feeder generation scriptsprovided by the GridLAB-D development team are used to automaticallygenerate a population of residential buildings characteristics based onfeeder nominal load characteristics and climate region.

Step 2) For each house, a base case load simulation involves thefollowing: A) A fixed cooling temperature setpoint is selected from adistribution. B) Using TMY and RECS data, the zone free-floattemperature for the current time period is found by simulating withoutoperating air-conditioning equipment. C) If the zone temperature exceedsthe cooling setpoint, the energy required to bring the zone back to thetemperature is calculated; if not, new mass and zone temperatures arecalculated. D) Energy consumption by the air-conditioning equipment iscalculated given the delivered cooling energy from each time step. TheROM is used for the calculations in steps (B) through (D). The base caseload includes air-conditioning, miscellaneous electric loads,appliances, and electric hot water heaters. Alternatively, other thanbase case simulation, Step 2 can be modified to simulate a load-shapingancillary service that is provided by GridMPC setpoint adjustment inresponse to forecast pricing.

Step 3) For each house, using the extended model, the calculation of thezone temperature in each time step enables a logic-based assessment ofwhether the conditioned space is at the upper or lower temperaturelimits of comfort. Subject to minimum run-time constraints, if the airconditioner is off and the zone temperature is between comfort limits,then load can be added. Similarly, if the air conditioner is on and thezone temperature is between comfort limits, then load can be shed.However, if the zone temperature is at the upper comfort limit, then noload can be shed because the air conditioner must run to keep the zonefrom overheating; likewise, if the zone temperature is at the lowercomfort limit, then no load can be added without over-cooling the zone.This on/off logic governs the calculation of instantaneousload-adding/load-shedding opportunities within temperature setpoints.

Step 4) Residential loads and instantaneous add/shed opportunities areaggregated at the feeder level using the R statistical programmingenvironment. Instantaneous add/shed opportunities in MW are then dividedby feeder demand in MW and expressed as a percentage of feeder load.

Step 5) The percentage load-add/shed results are transformed into aweighted average (on a per city basis) by multiplying the output of Step4 by the percentage of each type of feeder per city. To create anationwide perspective of instantaneous load-adding/load-sheddingopportunities, multiple representative feeders are simulated in nearlyequally spaced cities across the climate regions defined in thedistribution taxonomy in. For reference, a map of distribution taxonomyclimate regions is shown in FIG. 9, and a list of feeder weighting andcharacteristics are shown in Table 5.1. The regions are as follows:Temperate region 1, cold region 2, hot/arid region 3, hot/cold region 4,hot/humid region 5.

TABLE 5.1 Prototypical feeder weighting by region. # of % within RegionFeeder kV Feeders a Region Description Region 1 R1-12.47-1 12.5 2,20021% Moderate suburban and rural R1-12.47-2 12.47 2,500 23% Moderatesuburban and light rural R1-12.47-3 12.47 2,000 19% Small urban centerR1-12.47-4 12.47 1,800 17% Heavy suburban R1-25.00-1 24.9 1,200 11%Light rural GC-12.47-1 12.47 1,000 9% Single large commercial or Total10,700 industrial Region 2 R2.12.47-1 12.5 3,500 19% Light urbanR2.12.47-2 12.47 3,200 17% Moderate suburban R2.12.47-3 12.47 3,000 16%Light suburban R2.25.00-1 24.9 3,500 19% Moderate urban R2-35.00-1 34.54,000 21% Light rural GC-12.47-1 12.47 1,500 8% Single large commericalor Total 18,700 industrial Region 3 R3-12.47-1 12.47 1,500 30% Heavyurban R3-12.47-2 12.47 1,500 30% Moderate urban R3-12.47-3 12.47 1,00020% Heavy suburban GC-12.47-1 12.47 1,000 20% Single large commerical orTotal 5,000 industrial Region 4 R4-12.47-1 13.8 1,400 33% Heavy urbanwith rural spur R4-12.47-2 12.5 1,500 36% Light suburban and moderateurban R4-25.00-1 24.9 1,250 30% Light rural GC-12.47-1 12.47 750 2%Single large commerical or Total 4,900 industrial Region 5 R5-12.47-113.8 400 9% Heavy suburban and moderate urban R5-12.47-2 12.47 600 13%Moderate suburban and heavy urban R5-12.47-3 13.8 650 14% Moderate ruralR5-12.47-4 12.47 500 11% Moderate suburban and urban R5-12.47-5 12.47450 10% Moderate suburban and light urban R5-25.00-1 22.9 450 10% Heavysuburban and moderate urban R5-35.00-1 34.5 500 11% Moderate suburbanand light urban GC-12.47-1 12.47 1,000 22% Single large commercial orTotal 4,550 industrial TOTAL 43,850

It is critically important to note that following aload-adding/load-shedding event, the future operation ofair-conditioning cannot be controlled continuously. The resultingload-adding and load-shedding opportunities after participating in loadincrease and decrease events is discussed in Step 6.

Step 6) Lastly, as a separate activity, GridMPC evaluates thetime-varying load-shaping capabilities of homes reacting to a day-ahead5-minute electricity pricing forecast. A perfect forecast is assumedthat is based on recent residential market-cleared prices from, forexample, the ComEd Internet API. The ComEd Chicago market prices used inthis simulation are illustrative only and are not representative of therest of the United States. That said, just as per-city TMY data areavailable today, in the future it is expected that location-basedforecast marginal pricing will also be available and will be a criticalspatiotemporal input that is used to automatically shape residentialload to provide ancillary services throughout the distribution andtransmission grid.

5.4 Discussion and Results Analysis

This section presents results for load shaping opportunities inresidences and in electrical distribution feeders. At the end of thissection are results of feeder-level response in the context of MPC.

5.4.1 Single Residence Load Shaping Opportunities

An example of GridMPC load management optimization of residentialcentral air-conditioning reveals adjustments to the cooling setpointthroughout July 20, as shown in FIG. 10. Note the smaller changes insetpoint when the home is occupied and the larger changes in setpointduring the middle of the day when the home is expected to be unoccupied.

GridMPC air-conditioning setpoint in gold (solid black line), zonetemperature in blue (hashed line), and energy delivered (black bars)every 5 minutes on July 20, assuming a two-stage centralair-conditioning system with a 10-minute minimum run time. Applying thetemperature comfort constraint logic, we can obtain the instantaneousload-adding/load-shedding opportunities for the house every 5 minutes onJuly 20. It was found that because of comfort constraints, there are afew intervals when load cannot be added and many intervals when loadcannot be shed.

5.4.2 Feeder-Level Load Shaping Opportunities

To calculate base case feeder-level instantaneous load opportunities,fixed setpoints are constant in time, and add/shed results areaggregated every 5 minutes across 2,146 homes on the Houstonprototypical Feeder. Load-adding opportunities, with the top being themaximum possible instantaneous load, the base case whole-building load,and load-shedding opportunities, (with the minimum possibleinstantaneous load depicted by the top of the green area), wherecharted. After normalizing feeder-level results, the average percentageinstantaneous load-adding/load-shedding opportunities as a function ofwhole-building electric load every 5-minutes on July 20 based on thesame 2,146 homes on Houston Feeder was determined.

Thermal mass-enabled instantaneous feeder load-adding/sheddingopportunities every 5-minutes on July 20, expressed as percentage, basedon aggregated whole-building electric use was then tabulated. Theresults of combining feeder-level instantaneousload-adding/load-shedding opportunities on per city basis across theUnited States on July 20th was then observed. Distributional statisticsNationwide summary statistics appear at lower right were determined. Theresulting heat map of thermal mass-enabled U.S. residentialair-conditioning instantaneous percentage electricload-adding/load-shedding opportunities every 5 minutes on July 20^(th)showed the increased add/shed opportunities because of increasedair-conditioning loads in hot and humid southern climates, e.g.,Houston, Tex., and Jacksonville, Fla.

The corresponding instantaneous load-shedding opportunities during the5-minute interval at the top of each hour for all 24 hours of July 20was mapped for the minimum and maximum scale of −53% to 0% for theentire United States for loads over each hour of a 24 hour period andareas of shed were noted. Corresponding load-adding opportunities duringthe 5-minute interval at the top of each hour for all 24 hours of July20^(th) were observed with reference to a minimum and maximum scale of0% to 189% load-add.

A U.S. load-add contour map for all hours of July 20^(th) was generated.It was found that the amount of add/shed opportunities over time isproportional to the duty cycle of air-conditioning systems. An airconditioner with a low duty cycle (in cooler hours) has a lowopportunity to shed load and high opportunity to add load. Conversely,an air conditioner with a high duty cycle (in warmer hours) has a highopportunity to shed load and a low opportunity to add load. Themagnitude of add/shed opportunities is proportional to the size of airconditioners. The larger air conditioners required in hot climates havelarger compressors and circulation motors and hence provide increasedadd/shed magnitudes.

5.4.3 Feeder-Level MPC Control Response

The final step was evaluating the MPC load-shaping capabilities of 100%participating homes based on an assumed perfect forecast of day-aheadresidential 5-minute pricing and a deterministic supply of power fromthree generators, each providing up to 3 MW of capacity at differingmarginal costs. Simulation results of deviations were charted, depictingbase case and optimized loads every 5 minutes on July 20 based on thesame 2,146 homes on Houston Feeder. It was found that, in practice,price fluctuations and building responses would be based on the actualand forecast needs of the balance of system, not on Chicago marketpricing. Further, any air-conditioning setpoint adjustment hastime-lagged effects because the aggregate building responses are slowerthan the 5-minute price changes.

Then a single-day feeder-level response was modelled using the base casedemand, MPC-based response to forecast price signal, and themidnight-to-midnight 5-minute forecast price signal. It was found thatreductions in demand during high price periods. Depending on the needsof the grid, the oscillatory nature could be beneficial for providinggrid ancillary services, but, more likely, might be detrimental for airconditioners that are cycled on and off too frequently. Pricing-basedelectricity is available from many electric utilities and forecastdynamic electricity prices are increasingly available via the Internet.Savings attributable to ARLS are dependent on differences in pricingwhich vary by utility for industrial, commercial, and residentialcustomers. As shown in FIG. 11, residential electric rates vary by amultiple of 3 or more across the United States, highlighting the spatialnature and potential value of flexible residential building loads.

5.5 Conclusions

These experiments contribute to characterizing electric grid systembenefits of MPC-based residential load shaping. The spatiotemporalpotential is explored across the United States for residential buildingsto shape electric demand at the distribution feeder level by adding orshedding load to minimize electricity production costs. Air-conditioningand appliance loads in more than 100,000 homes on 204 distributionfeeders are calculated based on TMY weather data and a thermal housemodel that reflects geographic diversity in the building stock. Aweighted average of feeders is used to express results in each of 35cities. Depending on the city and 5-minute interval, thermalmass-enabled load-shedding opportunities up to 53% of load are possible,and load-adding opportunities up to 189% of load are possible.Instantaneous load-adding/load-shedding opportunities caused byair-conditioning are depicted as a function of geographical location andtime of day. Also included is a 24-hour simulation of feeder response toa residential day-ahead perfect forecast 5-minute pricing signal in thecontext of distributed MPC of air-conditioning load.

5.6 Throughout the equations cited in this application, the followingdefinitions shall apply:

In the building envelope expressed as a thermal model, for the glazing:

Ti is the zone dry-bulb temperature,

hgi is the interior film coefficient,

Rg is the glass thermal resistance,

hgo is the outdoor film coefficient, and

To is the outdoor dry-bulb temperature.

For the roof:

hri is the interior film coefficient,

Tri is the interior roof dry-bulb temperature,

Cri is the interior roof thermal capacitance,

Rr is the roof thermal resistance,

Tro is the outdoor roof dry-bulb temperature,

Cro is the outdoor roof thermal capacitance, and

hro is the outdoor film coefficient.

For the walls:

hwi is the interior film coefficient,

Twi is the interior wall dry-bulb temperature,

Cwi is the interior wall thermal capacitance,

Rw is the wall thermal resistance,

Two is the outdoor wall dry-bulb temperature,

Cwo is the outdoor wall thermal capacitance, and

hwo is the outdoor film coefficient.

For the floor:

hfi is the interior film coefficient,

Tfi is the interior floor dry-bulb temperature,

Cfi is the interior floor thermal capacitance,

Rf is the floor thermal resistance,

Tfo is the outdoor floor dry-bulb temperature,

Cfo is the outdoor floor thermal capacitance,

Rs is the soil thermal resistance, and

Ts is the deep soil temperature.

For the internal mass in the zone:

hi is the interior film coefficient,

Tm is the mass dry-bulb temperature, and

Cm is the mass thermal capacitance.

For the zone, Ci is the thermal capacitance.

Chapter 6

Estimating Value of Jointly Optimized Electric Power Generation andResidential Electrical Use

61 Introduction

This chapter is a culmination of research to estimate the value ofjointly optimized electric power generation and residential electricaluse. Discussed are efforts to transition from thermal generation to RES,the need for flexibility in electricity supply and demand, distributedstorage options, and electricity production costs. The concept of anoptimum load shape is developed along with a simulation framework forARLS. Results are presented and discussed from a case study of Texas.Certainly, other cities, states or provinces, and countries are withinthe scope of the invention.

Recent geopolitical initiatives to reduce carbon emissions haveencouraged research and development focused on clean and inexpensiveenergy sources. Initiatives have resulted in a series of policies andmandates designed to drive socio-economic trends to increase thepenetration of renewable energy sources (RES) and raise the efficiencyof existing generation. Despite these initiatives, greater than 75% ofthe world's electricity is still generated using thermal technology thatis on average 35-40% efficient. Thermal power plants cost billions ofdollars to operate on an annual basis. Furthermore, they are the largestconsumers of fresh water on the planet and are among the largestproducers of heat, creating nearly twice as much heat as they doelectricity along with greenhouse gases that trap heat. The transitionis not straight-forward and challenges exist in maintaining the securityof electricity supply as electricity providers seek to provide the mosteffective mix of generators, which include the highest penetration ofRES.

Electric load from the residential sector is forecast withever-increasing accuracy but has not traditionally been considered aspart of demand flexibility options. Residential loads are typicallyoperated as needed without regard for the physical constraints in agiven geographic area or the time-varying costs and CO2 emissions thatresult from generating electricity in thermal power plants. On thecontrary, this research focuses on end-use loads includingair-conditioning, domestic hot water (DHW) heating, and battery chargingthat are considered flexible due to the thermal and electrochemicalstorage ability of their inherent internal energy reservoirs. Throughload modulation, thermostats and other controllers of end-uses achievevarying levels of energy storage and release, subject to the constraintthat the systems they control remain sufficiently charged to maintainoccupant comfort and meet expected needs. The results and findingsherein extend to all consumer (demand) side loads, including commercialand business consumers of energy.

To determine the maximum theoretical benefit of load shaping, a dailyoptimum load shape ‘flattens’ the output of thermal generation over timein order to provide a best-case scenario for reducing variablegeneration costs. Ubiquitous Internet connectivity would allow energyretailers to broadcast future optimum load shapes to allow distributedstorage in end-uses and the operation of generation resources to beorchestrated in time by automatic residential load shaping (ARLS). InARLS, optimum load shapes modulate residential loads in concert withlowest cost generation in order to jointly optimize supply and demand byminimizing the production cost of electricity. To explore the value ofARLS across generation and load, models account for the variableelectricity production costs, emissions, and flow of electricity 602, asshown generally in FIG. 12.

FIG. 12 shows variable production costs, emissions, and electricityflows. The notation $, CO2/MWh denotes variable generation costs 602 andcarbon dioxide emissions per unit of energy. In addition to varying bygeneration mixtures, i.e., the mix of generators, the production costsof electricity also vary spatiotemporally (i.e., are impacted byweather), which simultaneously influences loads and, to a moresignificant extent, certain forms of RES generation. For example, duringsummer, higher wind speeds from a cold-weather front can simultaneouslydecrease the cooling load in homes and increase the output of wind powergeneration. At times electricity production cost can be relatively low,such as when wind and solar RES generate most of the required power. Atother times, the production cost can be high, such as when marginalpower is provided by expensive peaking generators that operate for onlya few hours a day, or from thermal generators operating at a partialload with lower heat rate efficiencies.

In joint optimization of electricity supply and demand, one objective ofARLS was flattening the net load met by thermal generators in orderraise the overall heat rate efficiency across the generation fleet andthus minimize variable production costs. Another objective of ARLS wasreducing the curtailment of low-cost RES by modulating loads to matchin-time the forecast availability of RES. The overarching goal of thiswork was to advance current trends to modernize generation ofelectricity by introducing ARLS which created load flexibility andelasticity thereby allowing for higher RES utilization, more efficientoperation of existing thermal generation, and more effective managementof distributed energy resources (DERs) including thermal and batterystorage.

The simulation framework was designed to apply to any area in the worldsubject to the availability of the following inputs attributes ofbuilding stock, end-use operating schedules, prototypical feeders,generator constraints, fuel costs, and time-synchronous historicalweather, load, and RES generation data. Once calibrated using historicaldata, many inputs to the simulation framework such as generation, load,weather, and RES penetration may be modified to support past- orfuture-based analysis. While necessary for optimizing the transmissionand distribution portions of the electric grid, spatial variations inthe production cost of electricity were not considered in this studythough should be considered in future work. This simulation Frameworktakes a system of systems approach to solving the problem of jointlyoptimizing electricity supply and demand. The novelty of this work isthe ability to provide estimates of the impact of ARLS on variablegeneration costs and CO2 emissions anywhere in the world using arelatively small set of input variables. Section 6.2 is an additionalliterature review of models for residential electric DHW heaters andbattery storage, section 6.3 describes the methodology, section 6.44discusses the results, and Section 6.5 presents conclusions and outlook.

6.2 Domain-Specific Literature Review

The author here considered a photovoltaic solar model, a reduced-orderthermodynamic building model, and the MPC of residentialair-conditioning. Further applicable models include residential electricDHW heaters and battery storage that were reviewed to inform addingdegrees of control to GridMPC.

6.2.1 Electric Domestic Hot Water Heaters

Benchmarks and illustrative methods were considered that are effectiveand reliable in analyzing the energy use of modern appliances andhouses. According to research, the energy savings for residential hotwater systems depends significantly on detailed occupant DHW usepatterns. Quantifying these patterns, as surrogate measures foroccupancy and energy usage, is essential for analyzing tank andtank-less water heaters, solar hot water systems with demand-side heatexchangers, distribution system improvements, and recirculation loops. Aseries of year-long hot water event schedules consistent with realisticprobability distributions of the start time, duration and flow ratevariability, clustering, fixture assignment, vacation periods, andseasonality, was analyzed.

Annual performance ratings for solar water heaters using TMY weather anda revised water draw criteria and model were reviewed. Bias stemmingfrom lack of realism in the then-existing ratings draw included 1) lowflow rates incorrectly boosted system performance with load-side heatexchangers; 2) low mains temperature incorrectly boosted performance forall solar water heaters, and 3) an invariant draw profile could notappropriately credit larger storage volumes versus smaller and did notportray realistic variations in the south to north geographies. Amore-realistic ratings draw was proposed that eliminated most bias byimproving mains inlet temperature and by specifying more realistic hotwater use. Current and the proposed draws and estimated typical ratingschanges from draw specification changes for typical systems in fourcities was reviewed. The average change in the ratings from the proposeddraw was approximately eight percent.

Two-node electric resistance water heater models are often used tocreate a balance between prediction accuracy and computation speed.Compared to a one-node model, a two-node model captures thestratification phenomenon in the tank, thus representing the outlettemperature more accurately. The following two-node electric domestichot water heater model in equation 6.1 yields:

$\begin{matrix}{{T_{\omega\; h}^{{lo}\;\omega}\left( {t + 1} \right)} = {\frac{1}{C_{\omega\; h}^{{lo}\;\omega}}\left\lbrack {{{UA}_{\omega\; h}^{{lo}\;\omega}\left( {{T_{air}^{in}(t)} - {T_{\omega\; h}^{{lo}\;\omega}(t)}} \right)} + {\Delta\;{m(t)}{C_{p}\left( {{T_{inlet}(t)} - {T_{\omega\; h}^{{lo}\;\omega}(t)}} \right)}} + {\eta_{\omega\; h}^{{lo}\;\omega}P_{\omega\; h}^{{nom},{{lo}\;\omega}}{U_{\omega\; h}^{{lo}\;\omega}(t)}}} \right\rbrack}} & (6.1) \\{{T_{\omega\; h}^{up}\left( {t + 1} \right)} = {\frac{1}{C_{\omega\; h}^{up}}\left\lbrack {{{UA}_{\omega\; h}^{up}\left( {{T_{air}^{in}(t)} - {T_{\omega\; h}^{up}(t)}} \right)} + {\Delta\;{m(t)}{C_{p}\left( {{T_{\omega\; h}^{1}(t)} - {T_{\omega\; h}^{up}(t)}} \right)}} + {\eta_{\omega\; h}^{up}P_{\omega\; h}^{{nom},{{lo}\;\omega}}{U_{\omega\; h}^{up}(t)}}} \right\rbrack}} & (6.2) \\{\mspace{79mu}{{T_{d\;\omega\; h}\left( {t + 1} \right)} = {T_{\omega\; h}^{up}\left( {t + 1} \right)}}} & (6.3)\end{matrix}$

where superscripts low and up represent the lower node and upper node ofthe tank.

Equations 6.1 and 6.2 calculate the water temperature as a function ofthe input variables.

T iwh is the water temperature and U iwh is the control signal of tanknode i in terms of duty cycle, T inair is the indoor air temperature,and Tin/et is the inlet water temperature. UAi is the product of theheat loss coefficient and surface area of node i, Δm is the flow rate ofhot water draws, Cp is the heat capacity of water, C whi is the thermalcapacitance of tank node i, and Pwh niom and niwh are the rated powerand efficiency of the resistive element in node i, respectively.Equation 6.3 indicates the temperature at which the hot water isdelivered by the top node of the water heater.

Their water heater model is subject to the following constraints:

T _(wh) ^(min) ≤T _(wh) ^(up) ≤T _(wh) ^(max)  (6.4)

T _(wh) ^(low) ≤T _(wh) ^(up)  (6.5)

U _(wh) ^(low) ≤U _(wh) ^(up)≤1  (6.6)

0≤U _(wh) ^(low) ,U _(wh) ^(up)≤1  (6.7)

where equation 6.4 dictates the constraints of the hot water temperaturefor safety reasons as the hot water exits the tank from the upper node.Equation 6.5 enforces the thermal stability in the tank such that thelower node should not be hotter than the upper node because of buoyancy.Equations 6.6 and 6.7 are the constraints of control signals U lowwh andU upwh which are continuous variables between 0 and 1 and can beinterpreted as duty cycles.

Though heat-pump water heaters provide savings in heating hot water andare increasing in popularity, they were not included in the literaturereview or analysis. That said, heat pump water heaters would likely havea) less instantaneous load shed capability due to reduced load from acompressor being used most often for heating versus a heating element,and b) similar load add capabilities when energizing a heating element.The literature reflects a general agreement on a) the importance of DHWdraw schedules as a proxy for energy use, and b) the use of two-nodemodels to capture the operating characteristics of DHW heaters.

6.2.2 Distributed Battery Storage of Electrical Energy

This invention considers energy storage cost and explore dispatchoptimization strategies to minimize costs associated with generatorstarts, generator fuel consumption, and battery erosion, based on athorough economic analysis of present worth life-cycle cost. Thisinvention considers the case when the net load is large enough and thusthe Genset fuel efficiency is high enough that the cost of dieselgeneration per unit of energy produced is less than the cost of batterywear; in which there is defined a critical load, Ld, above which thisapplies and develop a “Frugal Discharge Strategy.” The invention furthertakes into account metrics for comparing and sizing hybrid photovoltaic,wind, diesel, and battery generation in a stand-alone power system. Atechnoeconomic approach that combines two models, a reliability modeldeveloped beneath the total energy deficit concept and an economic modelbased on the calculation of total net present cost. The combinationdetermines the optimum configuration in the most cost-effective manner.Optimization results showed that a combined photovoltaic, wind, diesel,and battery system is more economically viable compared to either a) aphotovoltaic, wind, and battery system, or b) a diesel generator only.In a grid-tied battery system with dynamic pricing, added dimensions ofbuying and selling electricity at different prices at different times ofthe day helped make a case for local micro-controllers and new batterystorage operating paradigms.

In pricing-based DR, it is concluded that large loads could providenearly the same degree of flexibility for load-serving entities as doeslarge-scale storage if adequately incentivized. However, and this is asignificant caveat, there is more planning of lead-time required (i.e.,it is much harder) to extract flexibility from loads than from (battery)storage. Battery state of charge (SOC), charging power, Pch bat, anddischarging power, Pdis bat, are related as follows:

$\begin{matrix}{{{SOC}\left( {t + 1} \right)} = {{{SOC}(t)} + {\frac{\eta_{bat}^{ch}\Delta\; t}{Q_{bat}}{P_{bat}^{ch}(t)}} + {\frac{\Delta\; t}{\eta_{bat}^{dis}Q_{bat}}{P_{bat}^{dis}(t)}}}} & (6.8)\end{matrix}$

where Pch bat≥0, Pdis bat≤0, and ηcha bat, ηdis bat are the charging anddischarging efficiency of the battery system, Δ(t) is the length of theprediction step, and Qbat is the capacity of the battery. The batterycontrol variables are Uch bat=Pch bat=Pch,max batt and Udis bat=Pdisbat=Pdis,max bat(t) which represent the percentage of maximum chargingpower, Pch,max bat, and maximum discharging power, Pdis,max bat,respectively.

The battery system model in equation 6.8 is subject to the followingconstraints:

SOC^(min)≤SOC(t+1)≤SOC^(max)  (6.9)

0≤U _(bat) ^(ch)(t),U _(bat) ^(dis)(t)≤1  (6.10)

where equation 6.9 defines the operable SOC range for reducing batterydegradation and equation 6.10 indicates the range of the normalizedbattery control variables. In addition to thermal energy storage inbuildings and appliances, electrical energy storage in distributed fixedand mobile batteries is proliferating and introduces additional degreesof control for home energy management systems. Batteries are unique intheir ability to provide a near instantaneous response in load add andshed and can be very flexible over short time frames. In conjunctionwith one-time optimum sizing of a battery system and related chargingand discharging components, several factors that govern efficientcharging and discharging of batteries must be continuously considered inorder to provide optimum supervisory control.

The literature suggests that there are likely significant economicopportunities enabled by battery storage. This is especially so givenrecent trends away from net-metering where buying and selling costs areequal per unit of electricity, e.g., a kWh, toward feed-in tariffs,where selling cost is a fraction of buying cost. Lower feed-in tariffsgive rise to the need for optimum control that “buys low and sellshigh”.

6.3 Simulation Methodology

The ARLS simulation framework incorporates functionality for the modelpredictive control of buildings and the modeling of electricaldistribution feeders. The building thermal model in, as incorporatedinto GridMPC, was suitable for use without modification. However,GridMPC required extensions to provide for additional degrees of controlin order to optimize electrical energy use by DHW heaters and batterysystems. The GridMPC DHW heater required complete replacement in orderto allow for a) modeling thermal behavior, b) MPC-enabled setpointchanges, and c) usage schedules that reflect the empirical behaviorobserved in the Northwest Energy Efficiency Alliance, ResidentialBuilding Stock Analysis: Metering Study. The solar penetrationassumptions from GridMPC required changes to reflect 50% and 100% ofhomes having annual net-zero solar generation. A new model was requiredfor the MPC of battery charging and discharging.

6.3.1 Simulation Framework

The simulation framework utilizes a three-step process to estimate theimpacts on costs and CO2 emissions attributable to jointly optimizingelectric power generation and residential electrical use via MPC-basedARLS. In each step, a primary GAMS-based electricity production costmodel (PCM) simulated the costs and emissions of the thermal generatorsthat met the net load (the cost of the load without any management), anda second GAMS model determined the daily optimum net generation shape.In order to generate the optimum load shape, the RES was added to thedaily optimum net generation shape. MPC cases included the modelpredictive control (MPC) of various storage-capable end uses andscenarios included increasing penetration of RES.

First, actual costs, emissions, and optimum load shapes were estimatedbased on the historical net load (total load less RES generation).Second, simulated costs, emissions and optimum load shape were estimatedbased on the simulated historical net load obtained by coupling localhistorical weather and residential building stock data with thecalibrated thermodynamic residential building model. Results of theactual versus simulated historical load were compared to evaluate theskill of the simulation model. Third, costs and CO2 emissions wereestimated based on the simulated MPC of the on/off setpoints of end-useloads in various RES scenarios. In the second and third steps, theframework aggregated the simulated load from individual buildings byfeeder, city, and weather zone (also known as load zone). A high-levelrepresentation of the ARLS simulation framework proposed here is shownin FIG. 13.

In FIG. 13 an Automatic Residential Load Shaping Apparatus 601simulation framework 620 is depicted illustrating a consumer or demandside 622, a transmission network that includes transmission ofinformation and control signaling 624, and a power generation or supplyside 626. Load(i) denotes initial load. Load(f) denotes final optimizedload. Weather parameters include global horizontal irradiance (GHI),diffuse horizontal irradiance (DHI), and direct normal irradiance (DNI).Generator types include steam turbines (ST), combustion turbines (CT),combined cycle systems (CC), internal combustion engines (IC), andlandfill gas systems (LFG). Optimum load shapes are denoted by Shape(t).Variable production costs and CO2 emissions as a function of time arealso shown.

Starting at the left of FIG. 13, the consumer or demand side 622 isshown generally as a residence, however, any consumer side facility isconsidered applicable to the present invention(s) herein. In actuality,consumers are fed power through feeders of various stages, depicted bybounded boxes around the consumer facility. These include, for example,a zone wide feeder that feeds power to a group of consumers, typically2000 houses. Further upstream towards the supply side, there aretypically city wide feeders that distribute power to larger areas suchas cities and counties. The outer bounded box scales the load in termsof weather zones. In other words, an aspect disclosed herein is takinginto account loads, not only per geographic or demographic region, butper weather patterns, thereby allowing loads to more accurately reflectweather patterns in order to provide a more optimum load shape that isstable and less changing over time. Part of what is shown in this figureis the concept that the load shaping is performed at the grid level.Notably, the load shaping may be applied at any level, zone, city/countyor grid level, or at any level for that matter.

It should be noted that for purposes of evolving the presentinvention(s), regional parameters were selected for building stock.Next, auto-sizing based on local weather was performed for spaceheating, air-conditioning (HVAC), hot water heating, and solar PVsystems. Load simulation was performed per feeder, aggregated to cities,and scaled to weather zones, but may be simulated at any level. Dailyvariable production costs and optimum load shapes were calculated andbroadcast to MPC-enabled controllers in each home, which shaped loads tominimize cost based on forecast weather, occupant comfort constraints,and home/away schedules. Again, the optimum load shapes may becalculated in a similar manner at any granularity, residential or homezone, business facility or industrial zone, city, county, region, state,weather pattern area, etc., using the same inventive concepts laid outherein. In a specific example, PCMs performed a generation unitcommitment optimization in each simulation to minimize the variable costof generating electricity per day by choosing the lowest cost mix ofgenerators each hour, subject to the generator operating characteristicsand constraints in Table 6.1 below. Table 6.1 shows typical generatorconstraints used in production cost modeling. However, it shall beappreciated that generation unit commitment optimization(s) may beperformed in one or more simulations.

TABLE 6.1 Typical generator constraints used in production costmodeling. Characteristic Units Description Marginal heat rate MMBTU/MWhThe fuel burned by each generator to produce electrical output. Maximumgeneration MW The maximum output of each capacity generator. Minimumgeneration MW The minimum output of each capacity generator. Maximumupward MW/hour The maximum increase and and downward decrease in theoutput of each ramping generator in a single hour (note that thermalgenerators ramp slowly in comparison to gas turbines). Variableoperation $/MWh The VO&M for each generator, and maintenance whichincreases with output power. cost Startup cost $/start Related to thetype of fuel and time required to start each generator, typically from acold-start condition. Fuel price $/MMBTU Specific to each fuel type.Minimum downtime hours The amount of time required to constraint takeeach generator offline and back online again.

In the last step of the simulation framework, comparisons of load,costs, and emissions quantified the differences across all simulations.Of course, the comparison may be between any combination or permutationof simulations.

6.3.2 Electric Domestic Hot Water Heater Loads

While the above methodology provides solid data to base determiningoptimum loads, further improvements were performed. An evaluation wasperformed on the C++ based electric hot water heater physical modelavailable in GridLAB-D and found it lacking in realism. As a result, an‘instantaneous’ two-node physical model was created. The model ran on a1-second timescale, was written in Python code, and implemented the onand off logic 630 shown in FIG. 14.

FIG. 14 shows a state diagram of instantaneous DHW Heater. The model 630begins with in the state 632 with the water heater off. At state 634,the current temperature of the water heater is checked or determinedwhether it is below a set hysteresis point. If yes, then the waterheater enters the ON state 636. If not, the model returns to the state632. From the on state 636, it is checked or determined whether thecurrent temperature is above the set hysteresis point 638. If the resultis yes, then the state returns to the off state 632. If the answer is nothen the water heater stay in the on state 636. The model was generatedas code and was ported from Python to Java so that it could beincorporated into GridMPC. The Java version was verified against theoriginal python version by setting the same initial conditions (tankvolume and insulation characteristics) and runtime conditions (inletwater temperature, thermostat setpoint, dead band, and water draws) andthen verifying the energy consumption and water outlet temperature overtime.

A test was run to compare the results of simulation from the ported Javamodel to those of the Python model. Results of the two models were foundto be in agreement, and the Java model was incorporated into GridMPC. Inattempting to follow the daily optimum load shape, MPC adjusted thewater temperature setpoints causing electric water heaters to store andrelease thermal energy over time.

6.3.3 Distributed Battery Storage of Electrical Energy

The battery model was designed from modelling a hydraulic reservoirwhere water height represents the SOC. In general, house loads dischargethe battery and charge offsets loads; this is where the height ofreservoir analogy applies, e.g., if the load (out) is greater thancharge (in) then the battery discharges (water level drops).

At each time step, the GridMPC particle swarm optimizer (PSO) adjustedthe power supply control vector, which contained setpoints for the upperstate of charge and global lower bound. Battery discharge was equal tothe sum of all house loads, including air-conditioning, DHW heating, andappliances. Multiple runs were completed with various PSO simulationsettings to verify the desired operation in finding global versus localminima.

The battery was modeled with no standby losses (i.e., it maintainedcharge over time). State of charge was constrained to be equal to 50% atthe beginning and end of every daily simulation which: a) ensured thatbatteries were ready to charge or discharge at the start of simulationbased on Reference Demand, and b) simplified checksum calculations forthe conservation of energy. The battery model assumed a combined 89%round trip charge and discharge efficiency (100% also used duringtesting), no standby losses, and a maximum hourly charging rate of 25%of battery size. The battery was sized at 13.5 kW, as commonly found ina Tesla Powerwall. In attempting to follow the daily optimum load shape,provided by the instant invention, MPC adjusted the state of chargesetpoints causing batteries to charge and discharge over time to causethe battery to follow the optimum load shape.

6.3.4 Distributed Generation via Residential Solar PhotovoltaicCollectors

The solar model was modified for 50% and 100% PV penetration of homes.Solar array sizing for each house was based on annual net-zero energyconsumption. Each of the 14 unique feeders with 0% distributed solarphotovoltaic (PV) penetration was replicated once to include 50% ofhouses with PV and then again to include 100% of houses with PV. In the50% percent penetration case, every other house on a feeder was chosento have PV. The houses with PV were then kept as a static set whenperforming simulations. Reactive power control was not considered inthis research, but is within the scope of this model.

6.3.5 Key Performance Indicators

Metrics used to capture battery performance and the cost of controlincluded: a) NS, the number of charge/discharge sign reversals duringthe simulation, e.g., NS=3 for sequential intervals of +; −; +; +; −; −,and b) AV, the sum over the simulation of the absolute value of changesin the state of charge, SOC, e.g., AV=abs(+5%)+abs(−2%)=7% over twointervals. Both battery metrics were designed to measure how ‘hard’ abattery works, NS to aggregate charge cycles and AV to aggregate thetotal amount of energy passing through the battery over time expressedas a percent of battery capacity. Note that NN may rapidly exceed 100%,which is expected behavior. Both metrics are important in forecastingbattery life-cycle cost due to wear and tear from charging anddischarging. Battery charge, discharge, and SOC were stored at eachsimulation interval to allow for post-processing of results, e.g., tosupport analysis of deep discharge behavior.

In addition, a new summary metric, Ls, was developed to track the amountand percent of load shaped. Ls is defined as the sum over the simulationintervals of the absolute values of the deltas between the shaped andunshaped load and has units of energy. As a percentage, Ls became anormalized value when divided by the sum of energy delivered in theunshaped case.

6.3.6 Texas Case Study

The simulation framework was applied to a case study of the serving areaof the Electric Reliability Council of Texas (ERCOT). ERCOT was chosenas time-synchronous load and RES data are available, generator sizingand constraints are available, and for its significant electric load,equaling approximately 10% of U.S. electricity consumption on an annualbasis. The area simulated represented over 24 million residential,commercial, and industrial electricity customers across 200,000 squaremiles as depicted by the eight colored ERCOT weather zones ERCOT withinPNNL climate regions 3, 4, and 5 shown in FIG. 15.

FIG. 15 shows ERGOT operating area with eight weather zones (aka loadzones) denoted by colors (different shades) and three PNNL Grid Taxonomyclimate regions separated by dashed lines as shown. The case consistedof 1) unshaped and optimally shaped cases for actual and simulated ERGOTload, 2) seven combinations for the model predictive control (MPC) ofresidential air conditioners, electric DHW heaters, and battery chargingsystems, and 3) three scenarios of increasing RES penetration. Inaddition, the study included the operating characteristics andconstraints of 263 utility-scale thermal generators that closelyrepresent the ERGOT generation fleet, an excerpt of which is listed inTable 6.1. Note that generators were, for the most part, individual lineitems, though in some cases were grouped into a single-line metagenerator, e.g., utility wind and solar generators were grouped bytechnology. It shall be appreciated that the OLS methodology of thepresent invention may be applied per geographic region, environmentalregion, or weather zones, and the like.

Table 6.2 shows sample ERCOT generator characteristics and constraints.Prime movers include Combined Cycle systems (CC), Gas Turbines (GT),Landfill Gas systems (LFG), Steam Turbines (ST), Wind Turbines (WT) andPhotovoltaic (PV) generators. Not shown but also included in the ERCOTgeneration fleet are: Internal Combustion engines (IC) and CombustionTurbines (CT).

TABLE 6.2 Prime Capacity Marginal HB Base Heat Rate Co2Ems Unit CountyFuel Mover (MW) (MMBtu/MWh) (MMBTU) (lb/MMBtu) BRAUNIG_AVR1_CT1 bexarGAS CC 533.0 9.3 154.5 117.0 ATKIN_ATKINSG7 brazos GAS GT 18.0 12.8 0.0117.0

bexar LFG LFG 9.8 13.8 0.0 117.0 CALHOUN_UNIT1 calhoun GAS ST 44.0 12.3102.7 117.0 COLETO_COLETOG1 gollad COAL ST 655.0 10.4 1284.1 2.14.3CPSES_UNIT1 somervell NUCLEAR ST 1205.0 10.5 0.0 0.0 WT-ercot1 kinneyWING WT 20200.8 0.1 0.0 0.0 PV-ercot1 presidio SOLAR PV 1003.8 0.0 0.00.0 VOM MinLoad MinDown- Ramp- FuelPrice Unit ($/MWh) (MW) StartCost($)Time(hrs) Rate(MW/hr) ($/MMBtu) BRAUNIG_AVR1_CT1 3.7 233.2 49690.0 4169.5 3.3 ATKIN_ATKINSG7 15.7 7.2 419.5 1 6.2 3.3

8.9 3.9 456.8 4 3.4 0.0 CALHOUN_UNIT1 4.5 17.6 4102.0 7 10.2 3.3COLETO_COLETOG1 4.5 327.5 61063.7 12 117.2 2.2 CPSES_UNIT1 2.2 1084.5561693.2 20 96.4 0.7 WT-ercot1 0.0 0.0 0.0 0 20200.8 0.0 PV-ercot1 0.00.0 0.0 0 1003.8 0.0

indicates data missing or illegible when filed

Estimated production cost and emissions based on actual ERCOTelectricity use will now be discussed. For Case 1, Actual net load,production costs, and emissions were estimated for the 2005 hourly loadreported by ERCOT less the time-synchronous production of electricityfrom all utility scale wind and solar generators. The net load was metby thermal generation. The hourly GAMS (generic algebraic modelingsystem) PCM (production cross model) took as inputs the net load alongwith the generator characteristics and constraints. The PCM simulatedthe time-varying unit costs, marginal costs, and CO2 emissions based ona constraint of fossil-based thermal generation equaling net load foreach hour. Consistent with best practices, the simulated variableproduction costs were compared to the actual production costs for thesame period to check for general agreement.

For Case 2, a significant assumption was made to support the calculationof a) the minimum theoretical variable generation cost based on thedaily optimum thermal generation shape, and b) the daily optimum loadshape. The assumption was that all load could be shaped with negligible2 The 745 MW of Texas utility-scale hydroelectric generators wasconsidered small enough to exclude from the analysis, losses andpenalties. While unrealistic due to the efficiency losses of thermal andelectrical storage, this assumption allowed the daily-based GAMS PCM torelax the constraint of thermal generation equaling net load for everyhour to thermal generation equaling net load for an entire day. Thisalways resulted in a constant output ‘flat’ thermal generation shapewith no generator starts, stops, or generator ramping. The flat thermalgeneration shape had the lowest variable generation cost and thus wasconsidered the daily optimum net generation shape. As a final step inCase 2, the hourly-based PCM was re-run using the flat daily optimum netgeneration shape and returned the variable generation costs andemissions.

Estimated production cost and CO2 emissions based on simulated ERCOTelectricity use will now be discussed. For Case 3, Simulated Base Casenet load, the thermodynamic model of residential buildings, provided a5-minute time-series estimate for each of the 8 ERGOT weather zones andfor ERCOT in total. Individual cities in each of the 8 ERGOT weatherzones referenced the local airport time-synchronous weather denoted bythe shorted form of the International Civil Aviation Organizationairport identifier (e.g., Houston denoted by HOU). For weather details,see the 2005 annual files of hourly observations across Texas. Per thePNNL grid taxonomy, between four and eight of the 14 feeders unique toERCOT appeared in each city resulting in a total of 48 ‘city’ feeders,as shown in Table 2, where the letter R denotes residential feeders andthe letters GC denote generalized commercial feeders.

Table 6.3 shows ERCOT PNNL feeders by Weather Zone, city, and airport.

TABLE 6.3 ERCOT PNNL feeders by Weather Zone, city, and airport. WeatherZone City Airport Weather Feeders West Abilene ABI 4 R4-12.47-1/2,R4-25.00-1, GC-12.7-1 N. Central Dallas RBD 4 R4-12.47-1/2, R4-25.00-1,GC-12.47-1 Coast Houston HOU 8 R5-12.47-1/2/3/4/5, R5-25.00-1,R5-35.00-1, GC-12.47-1 Southern Laredo LRD 8 R5-12.47-1/2/3/4/5,R5-25.00-1, R5-35.00-1, GC-12.47-1 North Lubbock LBB 4 R3-12.47-1/2/3,GC-12.47-1 Far West Midland MAF 4 R3-12.47-1/2/3, GC-12.47-1 South SanAntonio SAT 8 R5-12.47-1/2/3/4/5, R5-25.00-1, R5-35.00-1, GC-12.47-1East Tyler TYR 8 R5-12.47-1/2/3/4/5, R5-25.00-1, R5-35.00-1, GC-12.47-1

The PNNL GridLAB-D MATLAB scripts populated the simulation files foreach unique feeder by selecting house attributes from the EnergyInformation Agency, Residential Energy Consumption Survey (RECS).GridMPC then used historical weather and the reduced-order thermalbuilding model to simulate hourly thermal and electrical load in homes.GridMPC simplifies each home in GridLAB-D into an equivalent ZIP loadmodel so that the homes within the feeder could be simulated simply asan electric demand calculated outside of GridLAB-D. This is accomplishedby first writing the electric demand of each home at each time step ofthe simulation into a separate file, then linking these files to thepower flow simulation using the GridLAB-D ZIPload and player objects.The new model that results, which combines the loads calculated byGridMPC with the GridLAB-D feeder model, is termed the ‘hybrid model andproduces GridLAB-D output files for each feeder.

Simulations of each of the feeders, including a complete set ofmiscellaneous loads and appliances were performed per house and thensummed to produce the aggregate loads per feeder without MPC control.This was referred to as the Base Case simulation and included the loadsof electric and natural gas water heaters, refrigerators, ranges,computers, televisions, cable boxes, and lighting. The distributionalstatistics such as sum and standard deviation of the per house 5-minenergy consumption and zone temperatures were calculated per day andthen aggregated across the simulation of all 46,384 houses. Referencingthe percent proportion of each feeder type within a region described,the feeder loads were summed proportionally to simulate the per day5-minute city loads.

In order to scale city loads up to create aggregate weather zone loads,the daily sum of the historical actual hourly weather zone load wasdivided by the daily sum of 5-minute city load in order to arrive at acity-to-zone scaling factor. City-to-zone scaling factors werecalculated for all eight weather zones and used as a multiplier of5-minute city loads in order to arrive at aggregate calibrated 5-minuteweather zone loads. The sum of loads used in calibration produced a zerobias (i.e., there was no residual in the energy balance); alternatively,calibration via non-linear minimization could be used to minimize thevariance between the actual and simulated loads using a Newton-typealgorithm with a non-zero bias. Lastly, the aggregate 5-minute load perweather zone was summed across all weather zones to create an unshapedBase Case (BC) aggregate 5-minute ERCOT load. FIG. 6.5 depicts the flowof power to weather zones, cities, feeders and houses.

FIG. 16 shows the flow 650, 650′, 650″ of electric power to weatherzones, cities (in this case Houston and Dallas), feeders, and houses.The varying line width illustrates the sizes of flows. Reading from thebottom to the top depicts aggregation. The plus symbols denote tens ofthousands of flows removed for clarity of chart.

As a final step in Case 3, the hourly-based PCM returned the variablegeneration costs and emissions for meeting the aggregated (unshaped) netload across ERCOT. Case 4, followed the same procedure as Case 2, inthis case, applied to the simulated load of Case 3. Cases 5-8 are thedaily excerpts from Cases 1-4 respectively.

6.3.6.3 Estimated Production Cost and Emissions Based on SimulatedMPC-Based Load Shaping

For Cases 9 through 15 of simulated shaped net loads, ARLS extended theMPC-based load shaping and air-conditioning models to include control ofelectrical charging of batteries and thermal charging of electric DHWheaters. Using ARLS, a set of cases and scenarios assessed the cost andCO2 impact of different combinations of controlled end uses, e.g.,air-conditioning only, air-conditioning plus battery charging,air-conditioning plus battery charging plus electric water heating.

Cases implemented the following steps: 1) MPC shaped electric load byoptimizing the above end-uses based on forecast weather, predeterminedpresence of occupants assumed to be away from home from 8 AM to 6 PM,bounded temperature setpoints, and target load shape deltas derived fromdaily optimum load shapes, 2) Loads were aggregated across Texas usingfeeder-to-weather zone scaling, and the residential load was estimatedto be 33% of total load with the remaining load assigned to commercialand industrial loads, 3) In three scenarios of RES penetration (A) low,(B) medium, and (C) high, the variable production costs and CO2emissions from generators operating to meet the MPC-managed load weresummarized.

6.3.6.4 MPC Scenarios

The MPC of air-conditioning followed a method with an auto-sized coolingcapacity based on the maximum cooling day for the year and a 10-minuteminimum on-time for single-stage air-conditioning. In attempting tofollow the daily optimum load shape, MPC adjusted the cooling setpointscausing houses to store and release thermal energy over time. In Cases9-15, MPC attempted to meet the daily optimum load shape, and theresulting shaped load was input to the hourly PCM, which returned costsand emissions for each ERCOT simulation scenario. For additional degreesof MPC control, particle swarm parameters were adjusted based on resultsof experiments to determine the appropriate parameters. The MPC controlintervals were increased from 30-minutes to 1-hour to limit theoscillatory behavior of loads and to reduce computer processing time.

6.3.6.5 PSO Optimization Parameters

The GridMPC air-conditioning model used an increment of 0.25 [K] and amaximum particle velocity of 0.25 [K]. To reflect allowable temperatureranges during home and away occupant hours, GridMPC was allowed toexplore a range of thermostat settings including 2 [K] below thesetpoint while the occupants were home, and from 5 [K] below to 3 [K]above the setpoint while the occupants were away.

The PSO parameters were set such that there were 24 dimensions, 1 perhour, for every controlled device, resulting in a total of 72 dimensionsfor the AC+BAT+WH case. The resolution of the PSO was set to 0.25 [K]for the air-conditioning and DHW heater models and to 1% of capacity forthe battery model. The maximum particle velocities were chosen bygraphing the swarm behavior for individual houses and inspecting graphsmanually, then choosing velocities which had a decent spread within 5000iterations. The maximum velocities for the AC, Battery, and Water Heaterwere 0.25, 2, and 24, respectively.

The Water Heater model had a range of −10 to +10 [K]. Given an incrementof 0.25 [K], the max velocity of the particles were 4 increments equalto 4/80 or 5% of the total search space for each dimension. The Batterymodel had a range of −50% to +50% from an initial 50% state of charge,with each value representing one percentage point of battery capacity.Given the increment of 1%, the max velocities of the particles were 24increments equal to 24/100 of the total search space for the first 20dimensions. Dimensions 20-24 had their lower and upper bounds decreasedby 12.5% each so that batteries would converge to 50% charge by the endof the day.

6.4 Results

In simulations of generation and load across the ERCOT serving area,cost and CO2 emission estimates for actual, simulated, and MPC-managedloads quantified the impact of various penetrations of utility wind,utility solar and distributed solar photovoltaic generation.Region-specific building envelopes, physics-based thermodynamic housemodels, and location-specific weather were used to forecast theday-ahead 5-minute time-series load per house, distribution feeder,city, and the ERGOT serving area. The forecasted load, RES generation,and thermal generator properties and constraints were combined toestimate electricity production costs and emissions based on theoptimized daily unit-commitment of the generation mix. Using the dailyoptimum load shape as a control signal, MPC enabled optimal supervisorycontrol of thermal and electrical energy storage in each house.Comparing the daily electric power production costs and emissions thatresulted from varying the number and type of storage degrees of freedomcontrolled by MPC, yielded a range of costs and CO2 emissions.

6.4.1 Cost and Emissions Overview

Table 6.4 summarizes annual costs and CO2 emissions for the ERCOTserving area. Rows depict different cases, and columns are grouped intothree scenarios of (A) low, (B) medium, and (C) high penetrations ofRES. Cases 1-4 summarize actual and simulated performance for 2005. Ineach group, the daily optimal load shape is applied to the actual andsimulated load to flatten net generation in order to determine thetheoretically lowest possible variable generation cost. The differencebetween the net load with and without the application of the optimalload shape determines the upper bounds of possible reductions invariable costs and CO2 emissions. Table 6.4 shows a full year range ofvariable generation costs and CO2 emissions for actual net load,simulated net load, and scenarios of increasing RES penetration. Entriesfor utility-scale wind and solar denote penetration based on annualproduction, e.g., uWind22 denotes utility wind providing 22% of theannual energy. Entries for distributed solar, e.g., dSolar50, denote thepercent of houses with PV.

TABLE 6.4 Scenarios A. Low RES penetration B. Medium RES penetration C.High RES penetration uWind22, uSolar1, dSolar0 uWind30, uSolar3,dSolar50 uWind38, uSolar5, dSolar100 Cases Cost Cost CO₂ Cost Cost CO₂Cost Cost CO₂ Full year 

$ [B] $/MWh lb [B] $ [B] $/MWh lb [B] $ [B] $/MWh lb [B] 1 Actually netload observed in Texas 5.36 17.96 252 3.75 12.58 1.16 3.22 10.77 94.7 2. . . daily optimum shape 5.31 17.80 257 3.23 10.83 1.48 1.92 6.44 77.93 Simulated BC net load 5.35 17.92 253 3.49 11.70 1.38 2.92 9.79 84.0 4. . . daily optimum shape 5.30 17.76 263 3.14 10.53 1.11 1.70 5.76 65.0Notes to Table 6.4: 1. Curtailment of uWind and uSolar is requiredduring some hours in Scenario B and many more house in Scenario C inorder to prevent over generation

Table 6.4, Scenario A, Cases 1 and 3 have good agreement between theannual cost of providing electricity Texas-wide, which was approximately$5.3B. Results from all Scenarios indicate a reduction in costs in Cases2 and 4 when the optimum load shape was applied. Scenario A savings were1%, Scenario B savings were approximately 10%, and Scenario C savingswere approximately 40%. Scenario B and C savings are particularlyimportant as they reflect the additional annual savings expected fromthe deployment of ARLS. Savings in Scenarios B and C are attributable toARLS shaping and modulating load to better match in time the availableRES, which results in decreased curtailment of RES.

With respect to CO2 emissions, Cases 2 and 4 have a 2% to 3% increasefrom Scenario A to Scenario B. This is possibly due to increased use oflower cost but higher CO2-producing coal steam turbines which displacedthe use of cleaner gas combined cycle generation. On the contrary,Scenario C provided an approximate 20% reduction in CO2 attributable toARLS' increased use of RES.

Table 6.5 summarizes the 1-day results for Cases 5-15, which isillustrative of Spring and Fall weather. RES penetration Scenarios A, Band C are the same is in Table 6.4. Cases 5, 6, 7, and 8 are 1-dayexcerpts of Cases 1, 2, 3, and 4 in Table 6.4. Cases 9 through 15quantify the performance of the MPC of air-conditioning, batterycharging, and electric DHW heating.

Table 6.5 shows the range of variable generation costs and CO2 emissionsfor actual net load, simulated net load, and scenarios of increasing RESpenetration.

Scenarios A. Low RES penetration B. Medium RES penetration C. High RESpenetration uWind22, uSolar1, dSolar0 uWind30, uSolar3, dSolar50uWind38, uSolar5, dSolar100 Cases Cost Cost CO₂ Cost Cost CO₂ Cost CostCO₂

$ [M] $/MWh lb [M] $ [M] $/MWh lb [M] $ [M] $/MWh lb [M] 5 Actually netload observed in Texas 12.96 15.45 486 6.7

8.02 1

3.67 4.37 52.00 6 . . . daily optimum shape 11.25 13.41 523 3.

4.32 119 1.97 1.28  8.00 7 Simulated BC net load 12.43 14.81 534 3.

3.66  42.0 1.97 1.28  8 8 . . . daily optimum shape 11.25 13.41 523 1.

7 1.28   8.0 1.97 1.28  8 9 Simulated net load with MPC A/C 12.7

15.17 518 2.84

.39  48.0 1.97 1.28  8 10 . . . with MPC BAT 11.89 14.17

2.50 2.98  38.0 1.97 1.28  8 11 . . . with MPC DWH 12.59 1

.01 562 3.06

.65  46.0 1.97 1.28  8 12 . . . with MPC A/C + BAT 12.20 14.54 576 2.643.14  39.0 1.97 1.28  8 13 . . . with MPC A/C + DWH 12.98 15.47 6

2.84 3.38  40 1.97 1.28 8 14 . . . with MPC BAT + DWH 12.12 14.44 5712.66 3.17  36 1.97 1.28  8 15 . . . with MPC A/C + BAT + DWH 12.63 15.05584 2.66 3.17  43 1.97 1.28  8 Notes to Table 6.5: 1. For cases 5-15,residentail PV solar sizing was initially based on net zero whole-houseenergy usage on an annual basis and then on daily basis to reducecompute times. 2. Curtailment of uWind and uSolar is required duringsome hours in Scenario B and many more hours in Scenario C in order toprevent over generation.

indicates data missing or illegible when filed

In Table 6.5 Scenario A, Cases 5 and 7 have reasonable agreement betweenthe daily cost of providing electricity Texas-wide, which wasapproximately $13M for the day. As summarized in Table 6.6, the greatestreductions in cost occur across all Scenarios in Cases 6 and 8 when theoptimum load shape was applied. Cases 9-15, Scenario A had positive andnegative impact of 4% or less. Negative impacts are due to 2%-3%increased energy use in optimizations due to standby losses associatedwith pre-cooling a home and pre-heating hot water. Cases 9-15, ScenarioB had positive savings impact of 19% or less with best results observedin the battery Case 10. Cases 9-15, Scenario C had no impact as RES andnuclear generation met the load in all Cases. With respect to CO2emissions, Scenario A indicates a 2% and 3% decrease in Cases 8 and 9,and an increase up to 12% for other Cases. Scenario B indicates an 81%decrease for Case 8 Daily Optimum Load Shape and positive results forCases 10, 12, and 14 involving the Battery. Other Cases had greater CO2emissions due to increased energy and possible increased coal generationthat displaced the use of cleaner gas combined cycle generation.Scenario C had no impact on CO2 emissions as RES and nuclear generationmet the load in all Cases.

Table 6.6 shows the impact compared to unshaped actual net load.

Scenarios Cost Impact [%] CO2 Impact [%] Cases A B C A B C 8 Net loadwith daily   9% 65% 0%   2%   81% 0% optimum shape 9 Simulated net loadwith −2%  7% 0%   3% −14% 0% MPC A/C 10 . . . with MPC BAT   4% 19% 0%  0%   10% 0% 11 . . . with MPC DWH −1%  0% 0% −5% −10% 0% 12 . . . withMPC A/C +   2% 14% 0% −8%    7% 0% BAT 13 . . . with MPC A/C + −4%  7%0% −12%  −17% 0% DWH 14 . . . with MPC BAT +   2% 13% 0% −7%   14% 0%DWH 15 . . . with MPC A/C + −2% 13% 0% −9%    0% 0% BAT + DWH

Table 6.7 summarizes the 1-day results for Cases 5-15, which isillustrative of a Summer peak demand day. RES penetration Scenarios A, Band C are the same is in Tables 6.4 and 6.5. As in Table 6.5, Cases 5,6, 7, and 8 are 1-day excerpts of Table 6.4 and Cases 9 through 15quantify the performance of MPC.

Table 6.7 shows the range of variable generation costs and CO2 emissionsfor scenarios of increasing RES penetration and increasing MPC of enduses.

Scenarios A. Low RES penetration B. Medium RES penetration C. High RESpenetration uWind22, uSolar1, dSolar0 uWind30, uSolar3, dSolar50uWind38, uSolar5, dSolar100 Cases Cost Cost CO₂ Cost Cost CO₂ Cost CostCO₂

$ [M] $/MWh lb [M] $ [M] $/MWh lb [M] $ [M] $/MWh lb [M] 5 Actually netload observed in Texas 25.14 22.51 1157 17.91 18.86  838 15.13 13.4 4716 . . . daily optimum shape 21.31 21.54 11

2 17.72 15.7  897 11.35 10.06 531 7 Simulated BC net load 31.83 28.21447 20.74 18.37 1003 13.44 11.91 482 8 . . . daily optimum shape 30.6927.19 1438 20.64 18.28 1017 11.66 10.33 557 9 Simulated net load withMPC A/C 30.52 28.81 1472 21.03 18.03 1016 13.02 11.54 511 10 . . . withMPC BAT 31.83 28.2 1453 20.54 18.2  979 11.97 10.61 478 11 . . . withMPC DWH 32.19 28.57 1457 20.8 18.43  983 13.46 11.93 529 12 . . . withMPC A/C + BAT 32.17 28.5 1467 20.9 18.52  995 12.33 10.92 515 13 . . .with MPC A/C + DWH 32.86 29.12 1400 21.17 18.75 1017 13.2 11.69 529 14 .. . with MPC BAT + DWH 32.15 28.48 1464 20.68 18.32  985 12.15 10.77 4

15 . . . with MPC A/C + BAT + DWH 32.65 28.93 1484 21.11 18.7 1006 12.4811.06 543 Notes to Table 6.7: 1. For cases 5-15, residentail PV solarsizing was initially based on net zero whole-house energy usage on anannual basis and then on daily basis to reduce compute times. 2.Curtailment of uWind and uSolar is required during some hours inScenario B and many more hours in Scenario C in order to prevent overgeneration.

indicates data missing or illegible when filed

In Table 6.7, Case 5 daily generation costs are less than Case 7, forScenario A, $25.4.M versus $31.8M and for Scenario B, $17.9M versus$21.7. However, Case 5, Scenario C costs are less than Case 7 costs. Thegreatest reductions in cost occur across all Scenarios in costs in Cases6 and 8 when the optimum load shape was applied. As summarized in Table6.8, Cases 9-15, Scenario A have zero or as much as −3% cost impacts,due to due to standby losses related to optimization. Cases 9-15,Scenario B had plus or minus up to % cost impacts. Cases 9-15, ScenarioC had up 114 to 13% positive cost impact.

With respect to CO2 emissions, Scenario A indicates a 2% and 3% negativeimpact. Scenario B indicates 1% negative to 2% positive impact. OtherCases had greater CO2 emissions due to increased energy and possibleincreased coal generation that displaced the use of cleaner gas combinedcycle generation. Scenario C had up to 16% negative impact due toincreased coal generation.

Table 6.8 shows the impact compared to unshaped actual net load.

Scenarios Cost Impact [%] CO2 Impact [%] Cases A B C A B C 8 . . . dailyoptimum shape   4%   0%   13%   1% −1% −16% 9 Simulated net load with−2% −1%    3% −2% −1%  −6% MPC A/C 10 . . . with MPC BAT   0%   1%   11%  0%   2%    1% 11 . . . with MPC DWH −1%   0%    0% −1%   2% −10% 12 .. . with MPC A/C + BAT −1% −1%    8% −1%   1%  −7% 13 . . . with MPCA/C + DWH −3% −2%    2% −3% −1% −10% 14 . . . with MPC BAT + DWH −1%  0%   10% −1%   2%  −1% 15 . . . with MPC A/C + BAT + −3% −2%  −7% −3%  0% −13% DWH

In summary, the benefits in load reduction are not apparent in many MPCCases for at least the following reasons: 1) There is increased energyuse due to the standby losses associated with shaping load. For example,preheating hot water incurs standby losses as the tank cools down. 2)The model is underpredicting high load periods. This behavior resultedin less use of the most expensive marginal generation, 3) The fullthermal generator fleet with a capacity of 69 GW was available to meet apeak load of 59 GW, as opposed to, say 10%, random unavailability due toscheduled and unscheduled maintenance and outages. This behavior alsoresulted in less use of the most expensive marginal generation. 4) Thethermal generator fleet was modeled using a constant heat rateefficiency. This behavior resulted in the same costs, for example, forthree similar generators running at 30% capacity to meet load versus onegenerator running at 90% capacity. This limitation would be apparentwhen the part-load operation of many generators is required whileawaiting a ramping event that could have been mitigated by ARLSattempting to meet the optimum load shape. Each of the above areaddressed as a potential for future work in Section 7.3.

6.4.2 Unshaped Actual Load versus Optimum Load Shape

For Cases 1 & 2, Scenario A, variable generation cost and CO2 emissionswere calculated for the unshaped actual hourly load and for the actualhourly load had it been optimally shaped, as shown in FIGS. 17 and 1818respectively. As expected, the daily optimum minimum cost generation wasachieved when the net load was constant, depicted as one or more fixedflat lines for each type of energy generation (referenced generally as662), as shown for each hour in FIG. 18. The curves labeled 664 are therenewable energy resources in this example. The net load in the industryis defined as the load of the non-renewable energy generators, such asnuclear, coal, gas, and oil generators. In FIG. 18 the net load isdefined for purposes of this application as the load of the thermalgenerator resources, i.e., nuclear, oil, coal, gas generators.

FIGS. 17 and 18 show ERGOT hourly generation based on the actual load atthe top (FIG. 17) and daily optimum load at the bottom (FIG. 18) on20-26 August On 22 and 26 August, 9 of the 10 generation technologiesshown here in use. There is no distributed solar (dSolar) generation inScenario A and hence none is depicted. Some generation colors are moreprevalent and easier to see. Of course, the present solution is notlimited to this selection of energy resources and may include others orsome of these may not be included in a particular emulation. This may bedependent on actual resources used or may be a selection by theemulation model. In addition, the renewable resources that are re-addedto the flattened load shape may be more or less than those renewableresources shown. The traditional or so-called thermal or “carbon” basedenergy resources (including nuclear) may be more or less than shownhere. Further, it may be chosen to flatten one or more of the renewableenergy resources in this model or no flatten some of the thermal orcarbon energy resources. The selection of which energy resources areflattened and which are not may depend on parameters such as sufficiencyor quality of data for a particular energy resource, ease ofcalculation, energy regulation definitions that redefine certainresources as renewable or thermal/carbon, selection by the client orenergy provider or distributor of energy, definition by the client orenergy provider or distributor of energy of what resources are renewableversus thermal/carbon energy resources, and predictability of a givenenergy resource (predictability, for example, is determinative ofwhether a resource can be flattened), for example.

In FIG. 18 there are a peak hours of dark red (GasCT) in-between thebands of orange (uWind) and light red (GasCC) on 22, 23, and 26 August,and there are peak hours of dark green (GasST) above dark blue (CoalsST)on 22 and 26 August. Barely visible are: 1) the smallest generationcontributions in the midday diurnal signature (d and u Solar) at thevery top of each graph, and 2) a continuous line (LFG) atop the hashedarea labeled (CoalST). In FIG. 17, note the up and down ramping of netgeneration (depicted by diurnal humps) of coal and gas as the Texasgeneration fleet varied its production of electricity to meet the netdemand. As expected, after calculating the daily optimum net generationshape, the ramping of net generation in 17 is removed, resulting in asmooth load in 18. Specifically, there is no intra-day ramping in thearea under the curve marked (CoalST) and (GasCC), which results in animpact on variable generation cost and CO2 emissions of individualgenerators. Summing across all generators and intervals, the totalenergy delivered each day in (a) and (b) is the same. Said differently,the areas under and including the topmost curves in FIGS. 17 and 18 arethe same.

As depicted in FIG. 18, calculation of the daily optimum generationsometimes resulted in greater than typical step changes on dayboundaries at midnight, e.g., between midnight on 22 August and 1 AM on23 August. Such atypical discontinuities were the result of adjacentdays having a different aggregate energy use and, as expected, wereminimal between days with similar meteorological conditions. Typicaldiscontinuities in load at midnight were defined as those observed inCase 1 (unshaped actual load) and were compared to the discontinuitiesin Case 2 (actual load had it been optimally shaped). Box plotdistributions of the midnight discontinuities in load in Cases 1 and 2provide a sense of typical versus atypical behavior per month.

By studying such box plots, the monthly median of midnightdiscontinuities is found to be less for the optimum versus the actualload in January, March, May through August, and November. Small midnightdiscontinuities are advantageous from the perspective of reduced thermaland pressure stresses that result from ramping thermal generators.Nonetheless, the upper and inter-quartile ranges in all months depictmany greater than typical midnight discontinuities. Methods for reducingmidnight discontinuities in load are likely to include modifications tothe GAMS PCM to manage day boundaries, are beyond the scope of thisresearch and should be explored. Hourly generation from the Texas fleetof RES and non-RES generators were compared and contrasted for the low,medium, and high RES penetration cases (Scenarios A, B, and C). Samplevisualizations of the load and the generation that met the load for eachhour are shown in FIGS. 18, 19, and 20, where Cases and Scenarios aredenoted with an abbreviated notation, e.g., C5SA, which denotes Case 5,Scenario A. In FIG. 18, both the FIGS. 19 and 20 visualizations are azoomed view from the weekly view depicted in FIGS. 16a and b ,respectively. In FIGS. 16-20, the legend indicates the type of energyresource which is found on the corresponding graph in the same order,such that nuclear is on the bottom and each subsequent energy resourcein the legend is layered upon the last.

FIG. 18 a and b shows Cases 5 & 6, Scenario A, ERCOT generation to meetthe unshaped load as shown in FIG. 19 at the top, and the optimallyshaped load in FIG. 20 at the bottom. FIG. 19 depicts the variability inload and generation in 24 hourly intervals. The variability in theutility wind resource (uWind 22) is denoted by the changing height ofthe bars labeled uWind30u, which was lowest from after sunrise throughhour 11. GasCT and GasIC generation were required for hours 14, 15, and16 to ramp up and meet the daily peak load. The top line in FIG. 18 bprovides visual insight to calculating the daily optimum load shape.First, the non-RES generation in FIG. 18 a was flattened by equallydistributing daily production needs across all 24 hours, in this casestarting with the bottom graph labeled (Nuclear) fleet up to andincluding the area under the curve labeled (GasCC) fleet. Second, thehourly RES generation was added atop the flattened non-RES generationresulting in a somewhat concave optimal load shape. It shall beappreciated that the traditional energy resources may be “flattened” by,for example, averaging the load for the thermal resources over a giventime period (or by other smoothing function), and that the renewableresources that are usually inflexible as to control of energy output (asolar panel provides energy only during the day) are not flattened, butadded to the flattened non-renewable energy sources that are moreflexible in their energy production and, therefore, can be controlled.

As shown in the legend of FIG. 19 a, Scenario B introduced: a) increasedutility wind (uWind) from 22% to 30% of the total annual ERCOT load, b)increased utility solar (uSolar) from 1% to 3% of the total annual ERCOTload, and c) 50% of homes having distributed net-zero solar PV.

FIG. 21 and b show Cases 5 & 6, Scenario B, ERCOT generation to meet the(FIG. 21) unshaped load at the top, and (FIG. 22) and optimally shapedload at the bottom. The impact on the non-RES generation fleet ofincreasing RES can be seen by comparing FIGS. 19, and 21. Note that FIG.21 shows an increase in ramping of net generation to accommodate theincrease in RES.

For the Daily Optimum, comparing FIGS. 20, and 22 provides insights intothe impact on the non-RES generation fleet of increasing RES. In FIG. 20the top of the non-RES generators is a flat line at 40 GW. In FIG. 22the top of the non-RES generators is a lower flat line reduced to 30 GW,representing a one-quarter reduction in the non-RES generation between

Scenarios A and B.

As shown in FIG. 23 and b, Scenario C further increased: a) uWind to 38%of the total annual ERCOT load, b) uSolar to 5% of the total annualERCOT load, c) dSolar to 100% of homes.

FIGS. 20 a and b shows cases 5 & 6, scenario C, ERCOT generation to meetthe (a) unshaped load at the top, and (b) and optimally shaped load atthe bottom. The black trace in (a) at the top denotes curtailed RES.

FIG. 23 is the forecast load shape or historical load bounded by theupper curve (incorporating the various power generation loads). Thehashings represent the different generators to meet the load asindicated in the corresponding legend. We take the forecast load shapeand subtract out the renewable component, represented by the areaslabeled dSolar50u, uSolar3u, uWind30u. The area that is left is met bythermal generators (and will get flattened as described above). In onemethodology, the area under the curve without the renewables isflattened. In one methodology, that area (the total energy of thenon-renewables) is divided by the number of intervals (here 24) toarrive at a load per unit time. This flattened signal or adjusted loadis provided to the thermal generators (the so called net generation).The renewable signature, i.e., that portion of the energy load fromrenewable sources, is put back on top of the flattened net, and thatgives you the optimal load shape as shown in FIG. 24 as generallyindicated by the arrows labeled renewables.

The additional impact on the non-RES generation fleet of furtherincreasing RES can be seen by comparing FIGS. 19, 21, and 23. Note thatFIG. 23) shows the greatest ramping of net generation to accommodate theincrease in RES. During daylight hours, the contributions of the RESgeneration required: 1) downward ramping through noon to preventover-generation, and then 2) upward ramping through hour 19 in order toensure supply would meet demand. Approaching noon, the required downwardramping was so great that the GasCC and CoalST fleets were completelyshut down by hour 11. During the afternoon, the generators in the CoalSTand GasCC fleets ramped up, and at hour 18 production was supplementedby fast-starting and fast-ramping GasCT and Gas IC.

For the Daily Optimum, comparing FIGS. 20, 22, and 24 provides insightsto the impact on the non-RES generation fleet of further increasing RES.In FIG. 24 the top of the non-RES generators is a lower flat linereduced to just over 20 GW, representing a nearly half reduction innon-RES generation between Scenarios A and C. The reductions in non-RESgeneration were enabled by shaping 21% of the load in Scenario A, 29% inScenario B, and 59% in Scenario C.

6.4.3 Simulated Load

For Cases 3 and 4, on an annual basis, the variable generation cost andCO2 emissions for the unshaped BC simulated load and for the shapeddaily optimum load in Scenarios A-C and were found to be in generalagreement with results of Cases 1 & 2, as shown in Table 6.4.Referencing Tables 6.5 and 6.7, Cases 5-8 are 1-day excerpts of Cases1-4. Historical electricity use was simulated using the building modelwith local weather inputs, scaled from feeder to city, and then city toweather zone. The actual and simulated load by weather zone was analyzedusing a new scheme 8 ERCOT weather zones. The two largest weather zonesare the Coast, in which Houston is located, and North Central, in whichDallas is located. Summing the historical observed load per weather zoneprovided a total ERCOT load which peaked near 60 GW during the middle ofthe week.

FIG. 25 and b show ERGOT load per weather zone. Actual load is shown atthe top (FIG. 25) and simulated load at the bottom (FIG. 26). Asexpected, the impact of outdoor temperature on load was found to besignificant. To investigate model prediction errors, histogram frequencydistributions were created to provide insight to the skill of the modelthroughout the forecasting regime.

The vertical axis denotes the number of hours in a year for load rangeson the horizontal axis. In FIG. 25, note the long tails in the actualload in the upper row that are missing in FIG. 26 bottom row which has areduced range of loads. The left of FIG. 26 depicts the total load andthe right shows the simulated net load after subtracting the actualtime-synchronous RES. To quantify whether the model was systematicallyunderpredicting or overpredicting the simulated load, the Mean BiasError was calculated for the year by subtracting the hourly actual loadfrom the predicted load, and was found to be zero.

Monthly boxplot distributions were created to compare the hourly errorsbetween simulated and actual load. It was observed that hourly residualerrors occurred between simulated and actual ERCOT load by month. Notethat the load is overpredicted in the Spring and Fall seasons andunderpredicted in the Summer. The mean and median of residual errors areleast in the Winter.

The best agreement between simulated and actual load in the Winter, overprediction during the Spring and Fall, and underprediction during theSummer was considered. To provide additional insight into thedistribution of residual errors, box plot distributions were created tocompare the hourly errors between simulated and actual load by the hourof day.

Residual errors between simulated and actual ERCOT load by the hour ofday were analyzed. It was found that the load is overpredicted in themorning before and after sunrise, underpredicted in the middle of theday, and overpredicted in the evening. The mean and median of residualerrors are least in hours 2, 3, 10, 19, and 24. A heat map like the onein FIG. 6 was used to depict residual errors by hour for each day overthe course of a year. It was found that the Spring and Fall versusSummer season behavior exhibited weak seasonal stationarity of residualsamong adjacent days as denoted.

FIG. 22 depicts 1) the greatest over predictions occurred in the Winter,Spring, and Fall seasons in the late afternoon and early evening, and 2)the greatest underpredictions occurred in the Summer in the lateevening. It was found that the summer evening simulated load decreasedfaster than actual load starting at hour 20. To further investigate theperformance of the model, the quantiles of simulated versus actualvalues were plotted against each other.

Quantile-quantile plots of simulated loads were overlayed with actualERGOT load. The black dots depict actual load, and the red dots depictsimulated load. In FIG. 27 the black lines labeled actual load depictactual load. The black lines labeled simulated load depict simulatedload, which is overpredicted at low loads and underpredicted at highloads. Looking back at previous data presented so far, there is evidenceto reject the assumption that the electric load data are normallydistributed. To simplify the interpretation of FIG. 27 the quantiles ofsimulated versus historical values were plotted against each other, asshown in FIG. 23.

As shown in FIG. 28 the residual errors of the model are depicted by thedistance from the diagonal. This visualization also indicates thatsimulated load is overpredicted at low loads and underpredicted at highloads. Lastly, a two-sample Kolmogorov-Smirnov Test was used to comparethe simulated and actual load for the year. The test is a nonparametricdistribution-independent evaluation comparing the simulated and actualsamples and is sensitive to differences in both location and shape ofthe empirical cumulative distribution functions of the two samples.Given a significance level of 0.05, the near-zero p-value of 2.2e-16provides evidence to reject the null hypothesis that the two sampleswere drawn from the same distribution.

A histogram of the residual errors are shown in FIG. 29. FIG. 29 shows ahistogram of errors between actual and simulated ERGOT load and may bethought of as an empirical distribution and normal distribution areoverlaid for reference. Comparing the previous figures, the residualerrors of simulated less actual loads are nearly normally distributed.Thus, it was found that the model overpredicts low loads less than itunderpredicts high loads. The impact of underpredicting high loads iscritically important as it introduces errors that significantly impactthe power systems planning process. First, it underestimates the amountof required peak generation capacity, which is likely the most expensivecapacity per unit of electricity produced. Second, it underestimates themarginal cost of generation during high-load and peak demand periods.Failing to predict the highest loads results in failing to simulate theoperation of the most expensive marginal generation, which results insignificantly underestimating the cost of high-load and peak demandperiods.

6.4.4 MPC Load Shaping

For Cases 9-15, MPC-enabled load shaping was simulated on individualdevices, with resulting loads, including generic loads, aggregated atthe house level. Depending on feeder size, between 168 and 2,192 homeswere aggregated to reflect the load at the feeder level. Device loads,generic loads, house loads, and feeder loads were recorded forverification of intended behavior and further post-processing. Forexample, the BC simulated load and the Reference Demand (scaled fromdaily optimum load shape) for Houston Feeder R5-2500-1 are shown in FIG.30.

FIG. 30 shows the base Base and Reference Demand for 2,146 homes onHouston Feeder R5-2500-1. In the figure, the Reference Demand informsGridMPC to add load when above the Base Case load until hour 10, to shedload when below the Base Case load between hours 10 and 21, and then toadd load again starting in hour 21 through the end of the day.Continuing the example, Feeder loads and Reference Demand werenormalized and then differenced to produce the daily optimum load shapedeltas, as shown in FIG. 31.

FIG. 31 shows the normalized Base Case, Reference Demand, and load shapedeltas for Houston Feeder R5-2500-1. In the figure, the green lineconnects the 288, 5-min load shape deltas, creating a zero-centeredinverse of the normalized load less the Reference Demand.

For Case 9, a simulated shaped load with MPC of air-conditioning (A/C),applying the daily optimum load shape deltas resulted in the optimizedload is shown in FIG. 32. The calculations for Cases 10-15 followed thesame process.

FIG. 33 shows a Base Case, Reference Demand, and MPC optimizedair-conditioning demand for Houston Feeder R5-2500-1. In FIG. 6.21, thecircle at hour 10 denotes MPC transition from load adding in the morningto load shedding in the middle of the day. Likewise, the circle at hour21 denotes MPC transition from load shedding in the middle of the day toload adding at night. In this example, there are two transitions denotedby circles, though the framework supports up to 288 transitions per daygiven the 5-minute interval used in the simulation. The specific timingand number of transitions per day varied depending on the simulated BCload and optimum load shape. In theory, given sufficient computationalresources, there is no upper limit on the number of transitionspossible. To simplify interpretation, the load curves in FIG. 33 werekept as smooth as possible by simulating the air-conditioning portion ofthe load (for these figures only) with infinitely variable airconditioners in each home that had no minimum on-time requirement.

On some days, the impacts of ARLS were negligible, slightly positive ornegative, such as 1) in Scenario A, when RES was fully utilizedregardless of the application of the optimum load shape, and 2) inScenarios B and C, when there was sufficient hourly RES throughout theday such that thermal generation was unneeded. On other days, theimpacts of ARLS were considerable and are detailed here.

The following examples were further examined for analysis of MPC-basedcontrol based on ARLS. The performance is shown for Cases 9-15,Scenarios A, B, and C in FIG. 33. The objective of GridMPC in all Casesand Scenarios was to shape and modulate load to match as closely aspossible the Feeder Reference Demand. This was accomplished by GridMPCminimizing the differences between the Optimized demand and FeederReference Demand.

The Feeder Reference Demand, depicted by the broken dot-dash line, wascalculated by scaling down the ERCOT daily optimal load shape such thatdaily energy use (i.e., the area under the curve) was the same as theBase Case energy use depicted in the solid line. In every MPC Case andRES penetration Scenario, the Feeder Reference Demand was the controlsignal used by GridMPC to add or shed load throughout the day.

From these plots, it is seen that Large excursions in theair-conditioning optimized loads at the start of each day denote initialcool/down of homes. Large excursions in the battery optimized load atthe start of each day denote a rapid change from the initial SOC of 50%and highlight the ability of batteries to immediately and rapidly chargeor discharge as directed by GridMPC in response to the optimum loadshape as delivered by Feeder Reference Demand. In addition, largeexcursions in the battery optimized load at the end of each day denoteGridMPC attempting to return the battery to a final SOC of 50%. Theseso-called ‘edge effects’ could be mitigated with a multi-day model,which would likely predict greater savings through more seamlessorchestration of air-conditioning and battery-enabled storage.

Performing these plots for different scenarios provides insight to thebehavior of ARLS on a spring day as annotated in the text following eachfigure. The behavior of ARLS on an ERCOT annual peak load day occurringin summer could be established. Higher loads that are driven byair-conditioning are apparent. As hypothesized in Section 3.2.2, the MPCof DERs can be complementary in supporting the grid at different timesof the day, as explained below.

FIG. 33 shows a Scenario A load shapes for Houston Feeder R5-2500-1.GridMPC attempted to increase the Optimized load above the Base Caseload until hour 9:30, decrease from hours 9:30-19:30, and increase fromhours 19:30-24:00. While the response in each of (a)-(g) is unique,similar load add and shed trends are apparent. The x-axis is labelled inincrements of 4 starting with 2, and the y-axis is labelled inincrements of 1 starting with 2. In another Scenario B load shapes forHouston Feeder R5-2500-1 were plotted. Here, the Feeder Reference Demandwas nearly flat. Fifty percent of homes having net-zero PV results inmid-day negative generation. GridMPC adds load to offset PV generation.Differing performance of load shaping are apparent in (a)-(g). InScenario C load shapes for Houston Feeder R5-2500-1 were plotted. Here,the Feeder Reference Demand specifies shedding load until hour 6 andadding load thereafter. All homes having net-zero PV results in greatermid-day negative generation. GridMPC adds load but is unable tocompletely offset PV generation.

In Scenario A load shapes for Houston Feeder R5-2500-1 were plotted.Here, load shaping benefits occur (a) in hours 1-22, and 6, (b) in hours1-18, and (c) in hours 1-7, 19, and 21. Although not an exactsuperposition of benefits, complimentary load shaping occurs, forexample, in hours 1-6 where the benefit in (e) is greater than in (a)and (c). In Scenario B load shapes for Houston Feeder R5-2500-1 wereplotted. Here, load shaping benefits occur (a) in hours 6-22, and 6, (b)in hours 3-22, and (c) in hours 7 and 13. Complimentary load shapingoccurs in (d) in hours 4-22, (e) in hour 7, (f) hours 3-8 and 19-21, and(g) with the smoothest optimized load. In Scenario C load shapes forHouston Feeder R5-2500-1 were plotted. Here load shaping benefits occur(a) in hours 11-13, and 6, (b) in hours 1-22, and (c) in hours 7 and 12.Complimentary load shaping occurs in (e) hour 7, (f) hour 8, and (g)with the smoothest optimized load. Undesired load add occurs in (d),(e), and (g) in hours 1-3.

An important takeaway from FIG. 33 and various Scenarios is thatresidential load can be shaped significantly in order to take advantageof increasing penetrations of RES. However, from a practical perspectiveand for the purposes of this study, the only loads than can be shapedare those with inherent thermal or electrical storage. In other words,load curves that correspond to thermal or electrical storage, namelynuclear, coal, oil, gas, and/or battery(ies) are flattened according tothe technique disclosed herein. To reiterate, flattening is aredistribution of the load for all or particular energy resource loadover unit time, which may include for example averaging, weightedaveraging, empirical redistribution, and the like. Significantlimitations arise when attempting to shape load from lighting,non-refrigeration appliances (i.e., other than refrigerators andfreezers), and miscellaneous electric loads (MELS) such as plug loads.Some of these energy resources may be omitted from the load shaping orapplication of the load shape to the appliance. MELS accounted forapproximately half of residential electricity usage in the RBSA meteringstudy.

6.4.5 Optimization Run Times

This section provides a brief overview and tabular summaries ofcomputational run times using the NREL Eagle high-performance computingcluster. In the Eagle standard queue, jobs may use up to a maximum of1,050 compute nodes. A single-scenario ERCOT ARLS simulation creates atotal of 304 jobs based on 38 Feeders multiplied by eight, one for eachof Cases 7 and 9-15. Requesting 304 compute nodes on Eagle would resultin the lowest start-to-finish runtime of approximately 45-50 minutes.However, given that jobs for smaller Feeders completed in less than 45minutes, time would be wasted when scheduling one Eagle node per feederfor the following reasons: 1) As smaller Feeder jobs completed, manycompute nodes would be idle and would remain unavailable for other useuntil all Feeder jobs completed. 2) Given the design of the Slurmworkload manager and job scheduler, large node requests would result inan extended time spent waiting in queue for the jobs to be scheduled tostart. As such, the most expedient and efficient use of computing timewas to request many more than one but fewer than 304 nodes, just enoughthen keep each node running short jobs until all the longer jobs hadfinished. This resulted in the lowest possible per-node computing cost.

PSO run time is a useful metric for comparing the computing timerequired for different Cases and different Feeders. PSO run times on theNREL Eagle high-performance computing cluster are shown in Tables 6.9and 6.10. Table 6.9 shows run times for completing simulations of 2,146homes on Feeder R5-2500-1.

TABLE 6.9 Typical PSO run times for Cases 9-15 on Feeder R5-2500-1 whichhas 2,146 homes. Case Time [sec] Time per home [msec] BASE 10 4.7 BAT 9745 AC 104 48 AC_BAT 206 96 AC_WH 707 329 WH 712 332 AC_BAT_WH 716 332BAT_WH 747 348

Differences in the time per house provide a sense of the complexity ofeach case. As expected, PSO run times increased with additional MPCdegrees of freedom. The most extended run times were observed in Casesthat included the DHW heater. PSO run times per feeder are shown inTable 6.10. Also included are the number of homes per feeder.

TABLE 6.10 Typical PSO run times for Case 15 AC_BAT_WH on all Feeders.Feeder Homes Time [sec] R5-1247-2 306 119 R5-1247-4 926 324 R5-1247-11,002 359 R5-1247-3 2,024 715 R5-1247-5 1,539 560 R5-2500-1 2,146 716R5-3500-1 2,192 724

As expected, PSO run times increased linearly, taking approximately 350milliseconds per home.

6.4.6 GridLAB-D Output Files

As part of the operation of GridMPC, GridLAB-D was called and createdoutput files that recorded typical power flow simulation metrics on15-minute intervals at specific locations on each feeder. For example,on Houston feeder R5-2500-1, the state of the physical switches in thedistribution network and the real, reactive, and imaginary voltages wererecorded for phases A, B, & C at the locations of specific capacitors,e.g., Capacitors 128, 129, 130, and 131. Other distribution networkmeasurements included: 1) Underground line losses, 2) Triplex linelosses, 3) Transformer losses, 4) Voltages at load tap changers 5)Overhead line loss, and 6) End of line voltages. An analysis of theGridLAB-D files is beyond the scope of this work and is suggested forfuture work.

6.5 Conclusions

The OLS model disclosed herein may be thought of as a simulationframework for creating broad geographic assessments of the impact ofresidential load flexibility on variable generation costs and CO2emissions for decision and policymakers. Unique to this was thecombination of physical models to estimate the impact of flexibleresidential load on the generation of electric power for the state ofTexas, which accounts for approximately 10 percent of the $100B annualelectric power production cost in the United States. The methodologyestimated the monetary savings that electricity producers would realizeby jointly optimizing the mix of generation and residential energy useunder various renewable energy penetration scenarios, which is anessential metric in deciding whether ARLS is worthy of further researchand implementation. Most importantly, the methodology is suitable forapplication to geographies around the world, requiring only knowledge orcollection of one or more of historical load, weather, attributes of thebuilding stock, operating schedules of electrical devices, distributionfeeder models, and generator constraints and/or fuel costs. In addition,the framework could be extended to consider the physical constraints oftransmission and distribution networks. Throughout its nearly 150 yearhistory, electric power generation has typically been optimized only tomeet the anticipated inflexible load and required reserves at the lowestpossible cost.

By including flexible residential load as an additional dimension ofoptimization, ARLS introduced a new paradigm in the traditionalsupply-demand relationship by managing storage-capable loads to shiftforward or backward in time in order to follow and use the least costlyforms of generation. The effect of time-shifting residential demand wastwofold: a) to reduce electric power production costs and CO2 emissionsby shaping load to increase the efficiency of thermal generation, and b)to decrease the curtailment of renewable energy sources (RES), thusforcing demand to seek and follow the least costly forms of supply allwhile providing for user needs and maintaining user comfort.

With the ability of ARLS to move generation away from more costlygenerators towards less costly generators, the Texas-wide annualopportunity for reduction in production costs increased as a function ofRES penetration. The maximum opportunity for savings in the high RESScenario C based on daily optimum load shapes were a ⅓ reduction inannual generation costs, from $3.2B to $1.9B, and a ⅕ reduction inannual CO2 emissions, from 95B to 78B tons. The scale of the generationchanges implies gross errors in modeling the sea change in generationsources and technologies. For example, in the presence of highlypenetrated RES, as fossil-fueled base-load, mid-merit, and peakingplants run less often, their marginal cost of generation will increase,likely skewing cost calculations in favor of ARLS as existing thermalgeneration becomes less competitive.

The inventive concepts herein shall now be discussed with reference toan actual example that applies one or more of the methodologiesdescribed herein whose results have been tabulated in Table 6.11 below.The table is arranged illustrating the time of day in increments of 1hour over a 24 hour period along the Y-axis, and the various stages ofprocessing the optimized load shape signal on the supply side andapplication of the OLS signal on the demand side. The dividing linebetween supply side and demand side is shown in the table, and may bethought of as a network over which the OLS signal is transferred. InTable 6.11, an electric car was used as an example and the signaling wasprocessed according to each stage as shown.

For illustrative purposes, this example will examine the first row, thatcorresponds to midnight. A forecast load in gigawatt hours is tabulatedin the first column, that may be considered as the total load for aparticular unit of area, which may be a micro-grid, such as a singledwelling or building, or a macro-grid, such as a region (geographic orweather defined), power grid, or sub-power grid, for example. It shallbe noted that the forecast load follows a shape as the load from hour tohour changes according to the needs of the consumers in the respectivedemand area. Of course, other values will reflect other grids and demandcurves. Similarly, in the next column, a forecast for the renewableenergy resources is provided. Both the forecast load and/or the forecastrenewables may be provided or generated according to the variousforecast methodologies already explained in detail above. The forecastsmay be based on actual load measurements, on a model of measurements, ora combination of both. In the alternative, the forecast for thenon-renewables may be provided, and any combination of forecast load,forecast renewables and/or the forecast non-renewables to obtain the netgeneration. In the current example, the forecast load for midnight istabulated as 36.1 GWh, and the forecast renewables for midnight istabulated a 6.0 GHh.

The next column provides the net generation, which is the amount ofenergy attributed to the non-renewable energy generator sources. In thetable shown, the net generation is obtained by subtracting or removingthe forecast renewables from the forecast or total load. Alternatively,the net generation itself may be obtained in other ways. For example,the net generation may be provided and the renewable component added tothat to obtain the optimum load shape. Returning to our example, the netgeneration is calculated as shown in the table to subtract the forecastrenewables of 6.0 GWh from the forecast load of 36.1 GWh to yield 30.1.The same is done over the remaining units of time for a given period(here 24 hours) to obtain the net generation per hour. In the next step,the net generation is flattened by apportioning a total energy, or loadrequirement, (here 845.1 GWh) over a period of time (here 24 hours),resulting in a distribution of 35.2 GWh, It shall be appreciated thatthe distribution may be apportioned using other methodologies such asthose already described, including weighting and empirical distribution.

The optimum load shape is created in this example by adding thecomponent for the renewable energy sources back onto the flattened loadshape, shown in the table as a percentage of load per hour (which addsup to 100% total load for the 24 hour period). In other words, thepercentage load for the optimum load shape per hour is the amount ofload the respective grid should be drawing, and the energy consumingdevices should draw energy at that percentage for that period of time.Of course, and as noted elsewhere, the energy consuming devices willadjust their load in an attempt to meet the percentage optimized loadbased on factors such as online time (particularly relevant for electriccars that are not connected to the grid 24/7 and other energy consumingdevices that charge and discharge simultaneously).

Table 6.11 separates the supply side (or energy generation side) fromthe demand side (or consumer/energy consuming device side) by a verticalgrey bar symbolizing the transmission route by which the optimum loadshape signal is transmitted. This transmission route may be a networksuch as the internet, a secure transmission route, telephone line, opticfiber, satellite network, static media such as a disk or USB stick, andthe like. It shall be appreciated that the optimum load shape isdetermined on the supply side in this example. However, this is due tothe availability and resources on the supply side to collect data thatis available and process the data from a vast source of forecast datausing computers and in some cases super-computers. In other words, thesupply side is best situated to generate the optimum load shape. In anyand all embodiments, the optimum load shape may alternatively begenerated by the distributor, a third party such as a supplier ofsoftware or power grid infrastructure, or locally at the residence orbuilding, and even by the energy consuming device itself. In that case,the optimum load shape may be created from forecast data, model data,actual data, or estimates from previous calculations of the optimum loadshape, for example, sent to the demand side entity determining theoptimum load shape.

Now turning to the demand side, the application of the optimized loadshape. It shall be appreciated that application uses the term optimumload shape and optimized load shape interchangeably, but it isrecognized that optimum may imply that a perfectly optimized load shapeis achieved. Recognizing that it may not be possible to achieve 100%perfection in the real world, the application refers to optimized inorder to express that the optimized load shape signal is an attempt toachieve the best possible load shape using the methodologies disclosedherein. To continue on the demand side, the 6th column in the tableshows the percentage of total load (10 kWh in our example) anddistributes it according to the optimum load shape apportionmentreceived (here labelled the electric vehicle EV optimum load shape). Itshall be appreciated that the optimum load shape is given in the tableas a percentage of the total load, instead of a signal value. Thisoperates a normalization on the optimum load shape, as a whole numbervalue may not be readily usable by the energy consuming device. It shallalso be appreciated that the signal representing the optimum (oroptimized) load shape may not necessarily be represented in percentages,but may be a signal of values, and that these values are converted intoa value the energy consuming device can use such as the percentage ofload shown in the table. One skilled in the art will understand readilyhow a smart switch or processor can calculate a value such as apercentage from a signal provided to it.

It shall be appreciated that some energy consuming devices may need tomake adjustments to the optimized load shape, or otherwise makeadjustments in how the energy consuming device operates based on, forexample, online connection to the grid or charge/discharge schedule. Inour example, the electric vehicle is not always connected to the powergrid and is not able to charge during unconnected periods. In that case,the optimum load shape received or operation/charging based thereon ismodified. As shown in the table, our example electric vehicle is notconnected to an energy source from 7:00 to 17:00 (7 AM to 5 PM),presumably while the owner is at work with the vehicle. This shown inthe table by the blocked out area during those times. In this case, theenergy consuming device, according to the inventive concepts laid out inthis disclosure, modify or recalculate the optimum load shapeapportionment according to its operating schedule. In any and allembodiments, this may be done as shown here by a reapportionment of thetotal load required (10 kWh in our example) over the time the vehicle isconnected to a power source. This may be achieved by generating apercentage proportional to the original percentage shown in column 5based on the amount of load that is not charged during the unconnectedtime periods. In our example, the EV optimum load shape is calculated tobe 7.3% of the load, which is the proportion of load not charged during7 AM to 5 PM corresponding to the 3.7% Optimum Load Shape shown incolumn 5. It shall be appreciated that the reapportionment of theoptimum load shape may be performed by a smart switch or meter, by theenergy consuming device itself, or the like as enumerated elsewhere inthis disclosure.

For comparison, the unshaped load for the electric vehicle EV is shownin column 8. In our example, the electric vehicle charges its entireload during hours 18:00 and 19:00 (6 PM and 7 PM). This is presumablybecause the electric vehicle operated without intelligence is plugged inwhen the driver returns home and the dumb vehicle simply begins tocharge until full. As will be appreciated, this causes all of the loadto be drawn over a relatively short period of time (2 hours),translating into a spike of demand at this time. Considering that mostdrivers of an electric vehicle return home around the same time, it isunsurprising that in actuality a large spike in the aggregate is causedduring this time period. It can be reasonably predicted that, as moredrivers turn to electric vehicles, the spike in electric demand duringthe early evening will be unmanageable in the near future. The inventiveconcepts laid out herein smartly redistribute the load where energy isprovided, thereby efficiently using the energy at the time when it isgenerated, which both allows traditional (thermal) energy generators tooperate at maximum efficiency and allows for the energy of therenewables to be fully utilized when produced (and not wasted).

In any and all embodiments, the optimized load shape signal may bemodified for a subset of the total load or entire grid such as a localregion, micro-grid (including a single building, residence), orappliance/energy consuming device. In some circumstances, it occurs thatthe demand or load for a subset of the total load or entire grid, ishigher or lower than that planned for by the determination of theoptimized load shape signal. For example, a spike in demand or load at aresidence or building may occur when more load is demanded, such as whenmultiple electric vehicles are charging at the same time. Anotherexample is that the residents or occupants of a building may be absentdue to a vacation or are in isolation and less power is being utilizedthan the planned for load determined by the optimized load shape signal.The spike or lull in demand may be defined as being a significantincrease/decrease in demand or load over a shorter time than the periodof the optimized load shape signal, and/or may be defined as being inaddition to or independently from time defined by a percentageincrease/decrease over the determined load indicated in the optimizedload shape signal. These fluctuations in demand/load may be detectedlocally by meters, including grid meters that are provided by, forexample, cable operators. Such grid meters are capable of connecting tothe Internet and providing grid metrics for a localized area on thegrid, and can be used to detect voltages/load of that area. In the caseof a fluctuation of the load for that area and in response thereto, theoptimized load shape can be modified, clipped, weighted or limited inorder to mitigate or suppress the spike or lull. In any and allembodiments, a location of the subset of the total load or entire gridsuch as a local region, micro-grid (including a single building,residence), or appliance/energy consuming device may be detected ordetermined. The location information may be determined on the demandside by the local region, micro-grid (including a single building,residence), or appliance/energy consuming device, or on the supply side(power utility or utility, infrastructure or IT supplier, ordistributor, for example, noting that a utility is a broader definitionof power utility that shall be broadly defined throughout thisdisclosure as an organization (including private and public) thatsupports, maintains or provides the infrastructure (including theequipment, network, or IT) for a public service. In any and allembodiments, the optimized load shape may be modified for that subsetarea as already described based on or in response to the determinedlocation or location information. For example, a single appliance orenergy consuming device may request or receive a modified optimized loadshape signal based on its location and/or based on the fluctuation ofdemand/load for that entity or local area.

Chapter 7

Conclusions and Future Work

This work provides estimates of the value of residential loadflexibility to support the transition to carbon-free electricity withoutfire. For understanding, carbons keep delivery of necessary andlegitimate distributors to renewable utilities mainly postponed. Theconcept of a daily optimum load shape was developed and appliedtheoretically and also as a control signal in residential MPC cases withincreasing penetration of RES. A data-driven approach was used to informa simulation framework designed for application in any area in the worldsubject to the availability of relatively few inputs. The followingsection briefly summarizes the results and conclusions drawn from thisresearch, followed by a discussion of potential areas of future work.

7.1 Summary of Results and Conclusions

After 30 years of pilot tests and sparse commercial deployments,management of residential demand continues, for the most part, viadirect utility control of load from appliances. However, direct loadcontrol has not evolved to provide support for integrating RES into thegeneration mix. While large-scale continuous optimum load shaping is anovel and promising solution for integrating RES, its impact is mostlyunknown. This work used simulations of the joint optimization of supplyand demand to assess the impact of ARLS and evaluate how theproliferation of Internet-connected thermostats, DHW heaters, andbattery charge controllers, could alter the traditional energysupply-meets-demand paradigm such that demand could be shaped tooptimally meet supply.

This work began with researching demand response programs andstatistical methods to quantify the diversity observed in real-worldempirical appliance measurements at varying spatiotemporal scales inorder to inform simulation models. To overcome limitations oftraditional stochastic methods in quantifying diverse, non-normal,non-stationary distributions, recent developments in spectral methodswere applied to capture and simulate load in the frequency and timedomains. The experiments in Phase 1 captured energy usage diversityrelated to unknowns that would be costly to ascertain on a mass scalesuch as building size and construction, varying numbers of buildingoccupants, occupant behaviors, and age of appliances. Specifically, theenergy usage statistics for electric DHW heaters were used to inform thefidelity of the models developed in Phase 2 concerning the timing of DHWuse.

In phase 1, a binary conditional algorithm was developed and applied toTCL appliance empirical time series data to estimate price-basedinstantaneous load add and shed opportunities. Key findings included 1)Simulated changes in electricity pricing resulted in instantaneous loadadd and shed opportunities which were quantified for individual andgroups of single-family homes in the Pacific Northwest of the UnitedStates. 2) Wavelet-based spectral analysis was superior in capturing,visualizing, and simulating diverse drivers of the non-Gaussian,non-stationary load.

Phase 2 involved working with GridLAB-D and GridMPC and creatingphysical models and simulations to estimate flexibility in electricaldemand provided by the MPC of air-conditioning, battery storage, andelectric DHW heating. A nationwide study of the MPC of air-conditioningincluded pricing-based control of an electrical distribution feeder. Abattery model was developed along with a DHW heater model designed toreflect the energy usage diversity observed in Phase 1. Key findingsincluded 1) Depending on the city, time of day, and 5-minute interval,residential thermal mass-enabled load-shedding opportunities up to 53%of load are possible, and load-adding opportunities up to 189% of loadare possible. 2) Air-conditioning setpoint changes have time-laggedeffects because the aggregate building responses are slower than the5-minute price changes.

In Phase 3, in order to estimate the value of ARLS, the flexibilitymodels developed in Phase 2 were explored in the context of the unitcommitment of the Texas fleet of 263 generators. Research tasks in Phase3 included 1) Modeling utility generation, distributed generation,distribution grids, and load across the state of Texas. 2) Jointlyoptimizing supply and demand by calculating and broadcasting optimumload shapes to appliances governed by MPC. 3) Estimating the maximumpossible impact in variable generation costs and CO2 emissions and thesubset thereof (if any) attributable to ARLS.

Key findings included 1) Given increasing RES penetration, ARLS raisedthe effectiveness of the generation-to-load system by decreasingoperating costs and CO2 emissions. 2) Electricity retailers could createload flexibility and elasticity by calculating and forecasting optimumload shapes, which encouraged electric loads to favor the lowest costthermal and renewable generators. 3) Through reception and processing ofdaily optimum load shapes along with forecast weather, thermostats andcontrollers for storage-capable end-uses were able to use modelpredictive control to automatically optimize their own on and offsetpoints in order to minimize the deviation from optimal load shapes.

7.2 Contributions

Data-driven analysis of empirical electricity usage data fromair-conditioning and appliances can aid in quantifying and simulatingdiversity in residential electric loads. A significant contribution ofthis work was the application and quantification of spectral methods tostudy and simulate appliance energy use behavior based on empiricaldata. Wavelet-based spectral analysis captured and visualized diverseand unknown drivers of load such occupancy characteristics and the type,age, and time of use of appliances. The performance of WARM-basedspectral methods was compared, and results provided insights intoquantifying diversity in energy consumption without a priori knowledgeof appliance details. The main contribution was that a robust simulationtechnique like WARM provides the ability to simulate energy use insynthetic subdivisions that is reflective of observed behavior. The WARMcan be used to simulate a variety of ensembles mimicking each appliancein order to aggregate statistics of energy usage by house and electricaldistribution feeder for potential decision making in managing the grid.In addition to the RBSA metering study in the Pacific Northwest of theUnited States, WARM and WARM-like simulation techniques could be appliedto datasets such as ecobee, Pecan Street and others in order to providesimulations for other climates and geospatial regions. While the WARMcan simulate unshaped behavior, it is unclear how to apply WARM tothermodynamic models that simulate shaped behavior.

Model predictive control that reflects the diversity observed inempirical data-driven models can aid in quantifying the end-to-endgeneration-to-load system benefits of automatic residential load shapingand modulation. A significant contribution of this work was thedevelopment and application of load add and shed models that quantifyload modulation opportunities based on the diverse appliance energyusage observed in empirical data. Instantaneous load add/shed estimatesprovided a sense of both the variability and the significant size ofopportunities possible, which spurred further research. The applicationof MPC added realism in estimating load add/shed opportunities in acontinuously controlled environment with constraints on occupantcomfort. Experiments in iterative approaches to pricing-based MPCprovided additional insights to price and load instability issues citedin the literature regarding challenges as high penetrations ofprice-takers become price-makers.

Combining the MPC of distributed energy resources with production costmodels, through co-simulation, can aid in estimating temporal valueacross a range of climate zones and geographic areas. The need toprevent instability while modulating load inspired the possibility ofdefining an optimal load shape that jointly optimized supply and demandby encouraging load to follow the lowest cost generation. To the best ofthe authors knowledge, this co-simulation has not been accomplished byothers and helps inform the economic justification of demandflexibility, in particular, flexible buildings. In addition, the MPC ofdistributed energy resources was found to be complementary in supportingthe grid at different times of the day.

7.3 Recommendations

7.3.1 Further Apply the Simulation Framework as-is

Several opportunities exist to apply the simulation framework as-is.

Model globally.

Given historical weather data, attributes of residential building stock,and grid taxonomy data already used in the framework, it is likely astraightforward exercise to extend the simulation to provide estimatesfor other regions of the United States. Statewide and nationwideestimates of reductions in variable generation cost and CO2 emissionscould be beneficial for investors and decision and policymakers.Geographies to consider modeling include the serving areas of theCalifornia Independent System Operator (CAISO), the MidcontinentIndependent System Operator (MISO), the Southwest Power Pool (SPP), thePJM Interconnect, the New York ISO (NYISO), and the New England ISO(ISO-NE). Also, expanding to a North America continental view, dependingon data availability, the framework could be applied to the powersystems in Mexico and Canada including the Alberta Electric SystemOperator (AESO), the Ontario Independent System Operator (IESO), andother entities. In addition, modeling all other areas of the world wouldprovide a global view of the opportunities afforded by ARLS. Efforts todo so could commence where time-synchronous historical load andgeneration data are available.

Model Changes in Load.

For clarity in results, the annual load was unchanged across all casesand scenarios. A next step is modeling the expected growth in load dueto combinations of reasons such as climate change and increasedelectrification of buildings, industry, and transportation. Increases inseasonal temperatures would increase the load, for example, fromair-conditioning. Another factor expected to increase load is theinductive charging of battery-powered devices, which is likely to becommonplace in all sectors and could have a significant effect,especially in transportation.

Model the Impact of Warmer Climates.

A potentially significant driver of change in thermal generatorefficiencies is increasing seasonal temperatures. Approximatelytwo-thirds of the energy used by thermal power plants is transferred asheat to the environment by way of heat exchangers. Warmer climatesreduce the efficiencies of heat exchangers, thus increasing fuelconsumption, heat and thermal emissions of power plants. The net effectwould be increased operation of thermal power plants for the same amountof electricity produced, and a worse outcome in the presence of higherelectricity needs. Decreases in thermal generation efficiency would be astraightforward addition to the simulation framework.

Model Uncertainty in Generation.

Opportunities to model uncertainty in generation include individualgenerator unavailability due to planned or unplanned outages, whichwould likely be a straightforward exercise. On a separate note, forfuture capacity planning, the impact of minor to significant changes inthe generation fleet could also be modeled. Changes in the generationfleet could result from retiring generators, re-firing coal generatorswith natural gas, and adding new generators.

7.3.2 Expand the Functionality of the Simulation Framework

Several opportunities exist to expand the functionality of thesimulation framework. Some opportunities are more straightforward toimplement than others. One opportunity may be to expand temporalfunctionality from daily to multi-day simulation. There are twohigh-level tasks to expand functionality from daily to multi-daysimulation, and both could improve model fidelity. In the temporalcontext, it is possible to extend the PCMs and GridMPC from daily tomulti-day simulation. For the PCMs, the multi-day simulation would allowmodeling of more realistic startup constraints on generators,particularly the longer start cycles typical of nuclear generators.Also, this multi-day simulation would ensure midnight discontinuities inload (and thus optimum load shapes) are reflective of typical behavior.For GridMPC, this multi-day simulation would allow for: a) relaxedconstraints on battery SOC at the beginning and end of the day, and b)midnight discontinuities that are reflective of typical behavior forbattery SOC, cooling zone and DHW temperatures.

Expanding marginal heat rate functionality from a single range tomultiple ranges, or to quadratic approximations is another opportunity.In the context of power generation, the PCM constraints, as implemented,specify each generator as having a fixed slope heat rate efficiency. Thework, however, makes possible a piecewise approximation of heat rate asa function of output power, which more accurately represents theefficiency over the operating regime of each generator. Additionally,the methods studied enable approximation of heat rate using quadraticfunctions. As such, the PCM fidelity could improve. Specifically, ARLScould take advantage of more efficient heat rates by modulating load tomaximize the efficiency of individual thermal generators.

Expanding transmission functionality from a single node to multiplenodes. In the context of transmission network constraints, the PCMsspecify delivery of power to a single transmission node which serves theentire region of study (e.g., all of Texas) with no transmission lossesor capacity constraints is another opportunity. The work, however, makespossible the use of a multi-node transmission network to representspatial interconnection constraints. Though out of the scope of thisstudy, the inclusion of transmission networks, would be useful inmodeling smaller portions of the grid and in modeling the value of ARLSin scenarios involving locational marginal pricing (LMP). LMP takes intoaccount the effect of actual operating conditions on the transmissionsystem in determining the price of electricity at different locationsand is expected to be increasingly important with growth in load andDERs.

Expanding functionality to add utility-scale storage is anotheropportunity. Recent developments in utility scale battery storage havedelivered profound effects on bulk power system operations, promptingnew storage-based ancillary services and significant economic marketchanges. As operational data become available, the simulation frameworkcould be extended to take advantage of utility-scale battery storage.

Expanding functionality to add other energy sectors and additionaldegrees of control is another opportunity. Adding commercial andindustrial loads to the simulation framework could enable estimating thevalue of the MPC of the loads in each sector, which together areresponsible for ⅔ of the load in Texas. In addition, enabling MPC ofspace heating within GridMPC would allow for year-round estimates of thevalue of HVAC control afforded by ARLS. Through HEMS, ARLS could drivedistributed control for various energy uses including operatingdishwashers, clothes washers and dryers, self-cleaning cycles ofelectric ranges, and other such tasks where one might not care so muchprecisely when a job completes as long as it is completed by within aspecific period. Due to computational complexity limits, while smallerloads such as home appliances and other IoT devices like mobile phonescould and should participate in ARLS, presently, it may not make senseto model each individually.

Expanding functionality to add combinations of load shaping techniques.While not widely deployed, dynamic electricity pricing may becomecommonplace in multiple sectors is another opportunity. As such,modeling the effect of combining dynamic electricity pricing and dailyoptimal load shapes could be explored.

Expanding functionality to explore the optimal size and use ofresidential batteries. The battery system modeled has an energy capacityof 13.5 kWh and an hourly charge rate of 25 percent is anotheropportunity. The impact on the grid-to-load system of various batterysizes and charge and discharge rates could be explored. Likewise, chargeand discharge strategies could be explored in the context of theexpected life cycle costs. In addition, ARLS would likely aid indistributed control of the charging of electric vehicle batteries.

Expanding functionality to explore varying specific heat capacities isanother opportunity. A sensitivity analysis could be performed toprovide insight as to how different amounts of thermal mass and phasechange materials could improve the efficiency of generation unitcommitment and economic dispatch. Adding mass or phase change materialsto buildings and appliances may enable, for example, hot water, chilledwater, and refrigeration systems to provide valuable flexibility inresidential, commercial, and industrial settings.

Expanding functionality to explore ARLS-enabled ancillary servicesExperiments could be performed to explore the possibility of providinggrid support in the presence of contingencies is another opportunity.There are no known practical obstacles to re-sending optimum load shapesfor near real-time execution. It could be a straightforward exercise tomodel the continuous updating of optimum load shapes.

Expanding functionality to explore spatiotemporal micro-area shapingLoad shaping has been simulated for all of Texas is another opportunity.The framework could be replicated and extended to shape multiple smallerregions. For example, with the expectation of a transmission ordistribution segment being overloaded, ARLS could modulate loadaccordingly to avoid spikes in LMPs. The monetary impact of not havingto increase transmission and distribution infrastructure could besignificant.

Expanding functionality to use different feeder taxonomies and modelsThe prototypical feeders developed were used for modeling U.S.distribution networks is another opportunity. The simulation frameworkcould be expanded to use other prototypical feeders for the U.S. and forother areas of the world.

Expanding functionality to adjust the scaling of aggregate load byseason is another opportunity. The simulation framework could beexpanded to scale the aggregate city-to-weather zone load based onWinter, Spring, Summer, and Fall seasons. For example, in summer, theload simulation model could better fit the data by using scaling thatreflects the high use of air-conditioning. After years developing,deploying and supporting cable broadband, Wi-Fi, and othercommunications technologies, the timing is better than ever to bringtogether telecommunications-based distributed control of electricitysupply and demand in support of transitioning to carbon-free energy.Over the years, in addition to the unprecedented growth of the Internetof Things, optimization tools and techniques have become available thatcan assist in orchestrating electrical supply and the demand ofindustrial, commercial and (hopefully soon) residential loads.

In the future, utilities and consumers can monetarily andenvironmentally benefit from continuously shaping load by alternativelyencouraging or discouraging the usage of electricity. The innovativeconcepts disclosed in this application is an important step to endingthe vast waste of thermal power plants, extinguish the massive firesrequired by such generators, and is the right timing to develop thisworking ARLS product.

8. Examples of the inventive methodologies disclosed herein shall now bediscussed.

An optimized load shaping apparatus for optimizing production andconsumption of energy includes a processor coupled to a computerreadable storage medium, wherein the computer readable storage mediumincludes a set of executable program instructions, which when executedcauses the processor to obtain information signals indicative of a firstload shape signal corresponding to a one of a total load, a renewableenergy (renewable energy supply or load) corresponding to one or morerenewable energy sources and a non-renewable energy (non-renewableenergy supply or load) corresponding to one or more non-renewable energysources of a serving area where energy. It shall be appreciated thatobtaining the information signals includes, for example, the informationsignals being sent to the processor, and/or generated by the processor.In any and all embodiments the processor may distinguish in the firstload shape signal between renewable energy. The renewable energy isenergy derived from natural resources that are replenishable, infiniteor inexhaustible, and non-renewable energy, and non-renewable energy isenergy derived from non-replenishable, finite or exhaustible resources.The processor is to remove a first component from the first load shapesignal corresponding to the renewable energy from a second componentcorresponding to the non-renewable energy to obtain a resulting loadshape signal, and flatten the resulting load shape signal byapportioning the resulting load shape signal across time intervals toobtain a flattened load shape signal. The processor is to add at least aportion of the first component corresponding to the renewable energy(supply or load) to the flattened load shape signal to create anoptimized load shape signal. As an alternative, or in addition to, theprocessor is to provide in any and all embodiments at least a portion ofthe optimized load shape signal configured to modulate electric loads ofenergy-consuming devices that consume energy. Providing the optimizedload shape may include transmitting the optimized load shape to aswitch, smart switch or energy consuming device on the demand side.

It shall be appreciated that a total load, is the total load for acertain area of the power grid, which may be a subset of the particularpower grid considered, including a macro grid or micro grid. It shallalso be appreciated that the flattening in any and all embodiments maybe through apportionment or by weighting of one or more time periods orone or more types of energy resource as mentioned elsewhere in thisdisclosure, but also through normalizing or normalization of the load.Further, it shall be appreciated that the renewable energy andnon-renewable energy, respectively, is the amount supplied or to besupplied (referred to as simply supply), which when looked at anotherway is that part of the total load comprising the renewable energy ornon-renewable energy. It shall further be appreciated that provide atleast a portion of the optimized load shape signal configured tomodulate an electric load of one or more energy-consuming devices thatconsume energy means that the optimized load shape signal is arranged orconstructed to offer a different load to the energy-consuming devicethan the load shape that the energy-consuming device was followingpreviously such as a historic load shape or a load shape based on theuser of the energy-consuming devices load habit. It shall be appreciatedthat the net generation load may be in any or all embodiments provideddirectly to the processor, or based on previous net generationinformation or calculations. Further, the processor may not need todistinguish between renewable and non-renewable energy components.

The optimized load shaping apparatus of any and all embodiments providesthat the first load shape signal corresponds to an actual load of aserving area obtained from a grid such as a micro-grid or a macro-grid,wherein the micro-grid is a stand-alone or grid connected system withlocal power supply and consumption, and the macro-grid is not astand-alone system and is connected outside local power supplies. Alocal power supply is, for example, a single residence or building thatprovides its own power either entirely or partially, such as from solarpanels, an electric vehicle, or local generators.

It shall be appreciated that the objective of optimizing the load shapeis to maximize an efficiency of one or more non-renewable energygenerators, and particularly to maximize the use of renewable generatorswhile maximizing the efficiency of non-renewable (including thermalgenerators). The optimized load shape signal is calculated, either atthe supply side, demand side, or at a quasi-supply side such as adistributor of energy, and is employed by energy consuming devices onthe demand or consumer side. The resulting use of power on the demandside, either as a single device, group of devices, or in the aggregate,such as on a feeder basis or larger region or environment region orgeography, results in a corresponding energy draw upstream on the supplyside that translates into usage by those generators. Those generators,particularly the non-renewable generators that can be flexibly drivenirrespective of natural events such as the weather or time of day, as aresult are deployed on a steady state basis, that is at their maximumefficiency for the demanded load, and are not ramped up and down,causing wear and tear on the equipment as well as saving immense cost ofenergy in spinning up those assets. The renewable energy generators,those that are not flexible (inflexible) or depend on the environmentsuch as the weather or time of day, are then free or capable to generateenergy at their normal operating conditions and times, that is withoutstrains caused by over supply. In other words, since the renewableenergy sources provide energy regardless of demand, the presentsolutions provide for efficient use of the energy that is generated bythe renewables, i.e., the energy that is generated regardless because ofthe environment (sun, wind, ocean power), and does not allow for wasteof that renewable energy, which may occur under the traditional supplyand demand on load as those users may use power at times other than whenrenewable sources are creating energy. This can be seen in FIGS. 19 and20 where the renewable portion is graphically shown to be “drivenupward” from FIGS. 21 to 22 and 23 and 24, respectively.

The optimized load shaping processor in any and all embodiments isintegrated into a device such as a computer, Graphical User Interface(GUI), cloud-based energy controller, dashboard, smart meter,thermostat, home energy management system, smart phone, data center,cloud, appliance, battery, and electric vehicle/electric vehiclecharger, for example.

The optimized load shaping in any and all embodiments bases the firstload shape signal on one or more of information such as a forecastsignal that forecasts load of the serving area, a pre-defined forecastsignal, and/or a model forecast/predicted signal.

The optimized load shaping in any and all embodiments generates therenewable energy from one or more of renewable energy generators such aswind, solar, hydro, geothermal, ocean, chemical, biochemical, closedhydrogen system, and/or battery energy sources. It shall be appreciatedthat replenishable resources are considered herein as those resourcessuch as traditional resources like wind, solar, hydro, geothermal, andmay further include replenishable resources for modern source of energysuch as ocean, chemical, biochemical, closed hydrogen systems, and/orbattery energy sources. Resources such as coal, gas, oil and nuclear areconsidered non-replenishable in the sense that their quantity is limitedon this earth. A closed energy system, including closed hydrogen systemsrefers to those energy sources that are replenished by re-energizing theenergy source, such as in a closed hydrogen system where hydrogen isburned resulting in water and the water molecule is split back intohydrogen and oxygen in order to obtain hydrogen again as a fuel.

The optimized load shaping processor in any and all embodiments is toflatten the resulting load shape signal for thermal non-renewablegenerators by apportioning the total energy over a time period to obtainan amount of load to be apportioned to that time period.

The optimized load shaping in any and all embodiments weights at leastone or more portions of the optimized load shape signal are weighted upor down, and for any energy generator, depending on the mix of renewableand non-renewable generation available. The result of weighting up ordown effects the allowance that a load may be higher or lower for aparticular time period, or for a particular generator or type ofgenerator. The weighting may also be set for one or more energyconsuming devices on the demand side, such as to encourage ordiscourage, or allow or disallow, energy consumption. Encouraging ordiscouraging (or allowing/disallowing) energy consuming devices tooperate at a weighted load may be based on credits or tokens that theconsumer earns for operating energy consuming devices at the optimizedload shape or credits or tokens that are purchased. The credit or tokenin any and all embodiments is produced corresponding to at least aportion of the optimized load shape signal.

Weighting, credits or tokens in any and all embodiments, provide amanner in which compliance with the OLS can be maintained. It shall beappreciated that compliance can be described as minimizing thedifference between the actual load shape and the OLS. When thedifference is zero, than the actual load shape has exactly followed theOLS. As mentioned in other sections herein, an optimized load shapesignal is generated that best approximates the optimal load shape,bearing in mind that anything optimum in the real world may not beachievable given, for example, imperfect data, freshness of the data,etc.

In other words, the optimized load shaping may select which resourcescan be operated or should be operated at a higher consumption. Asmentioned, in any and all embodiments this could be instances whereenergy is bought or sold on the market, for example by an (ISO)Independent System Operator. Such operators may make small or largeincreases in power at that time and shave the other periods in order toadjust for operating conditions, that is, whether generators are onlineor spinning up. This also allows operators, such as ISOs, to use orgenerate power when it comes available.

The optimized load shaping in any and all embodiments also encompasses amethod for optimizing production and consumption of energy. Obtaininginformation signals indicative of a first load shape signalcorresponding to one of a total load, a renewable energy (correspondingto renewable energy supply or load) corresponding to one or morerenewable energy sources and a non-renewable energy (corresponding torenewable energy supply or load) corresponding to one or morenon-renewable energy sources, wherein renewable energy is energy derivedfrom natural resources that are replenishable, infinite orinexhaustible, and wherein non-renewable energy is energy derived fromnon-replenishable, finite or exhaustible resources. It shall beappreciated that the method in any and all embodiments may distinguishbetween the renewable and non-renewable components, or it may be sentthe distinction in the form of, for example, signals. Removing a firstcomponent from the first load shape signal corresponding to therenewable energy load from a second component corresponding to thenon-renewable energy obtains a resulting load shape signal. Flatteningthe resulting load shape signal is accomplished by apportioning theresulting load shape signal across time intervals to obtain a flattenedload shape signal. Adding at least a portion of the first componentcorresponding to the renewable energy load to the flattened load shapesignal creates an optimized load shape signal. In any, all or none ofthe embodiments, the method may provide at least a portion of theoptimized load shape signal configured to modulate electric loads ofenergy-consuming devices that consume energy.

In any and all embodiments of the method the first load shape signalcorresponds to an actual load of a serving area obtained from a gridsuch as a micro-grid and a macro-grid, wherein the micro-grid and macrogrid are explained above.

In any and all embodiments the method maximizes efficiency of thenon-renewable generators, and in particular use of renewables whilemaximizing the efficiency of thermal generation.

In any and all embodiments the method bases the first load shape signalon one or more of information such as a forecast signal that forecastsload of the serving area, a pre-defined forecast signal, and/or a modelforecast signal.

In any and all embodiments the method flattens the resulting load shapesignal by apportioning the total energy over a time period to obtain anamount of load to be apportioned to that time period.

In any and all embodiments the method weights at least one or moreportions of the optimized load shape signal up or down for any timeperiod, and for any energy generator. The result of weighting up or downeffects the allowance that a load may be higher or lower for aparticular time period, or for a particular generator or type ofgenerator. The weighting may also be set for one or more energyconsuming devices on the demand side, such as to encourage ordiscourage, or allow or disallow, energy consumption. Encouraging ordiscouraging (or allowing disallowing) energy consuming devices tooperate at a weighted load may be based on credits or tokens that theconsumer earns for operating energy consuming devices at the optimizedload shape or credits or tokens that are purchased. The credit or tokenin any and all embodiments is produced corresponding to at least aportion of the optimized load shape signal.

In other words, the optimized load shaping may serve to select whichresources can be operated or should be operated at a higher consumption.As mentioned, in any and all embodiments this could be instances whereenergy is bought or sold on the market, for example by an (ISO)Independent System Operator. Such operators may make small or largeincreases in load at that time and shave load during other periods inorder to adjust for operating conditions, that is, whether generatorsare online or spinning up. This also allows operators, such as ISOs, touse or generate power when it comes available.

In any and all embodiments the method produces a credit or tokencorresponding to at least a portion of the optimized load shape signal.

In another example, in any and all embodiments a computer readablestorage medium is provided having stored thereon a program having aprogram code for performing the method and/or any or all of theembodiments.

In another example, an optimized load shape switch apparatus is providedfor optimizing production and consumption of energy. A processor coupledto a computer readable storage medium, wherein the computer readablestorage medium includes a set of executable program instructions, whichwhen executed causes the processor obtains to create optimum load shapesignal that represents a first load shape signal corresponding to atotal load of a serving area where energy is provided that has a firstcomponent of the first load shape signal corresponding to non-renewableenergy load flattened by an apportionment and a second component of thefirst load shape signal corresponding to renewable energy load added tothe first component was flattened. In any and all embodiments, renewableenergy is energy derived from natural resources that are replenishable,and wherein non-renewable energy is energy derived fromnon-replenishable resources. The processor in any and all embodimentsmay provide a switching signal based on at least a portion of theoptimized load shape signal configured to modulate an electricconsumption of an energy-consuming device in accordance with theoptimized load shape signal.

It shall be appreciated that the inventive solution(s) provided hereinmay be incorporated into the energy consuming device itself or a smartswitch or like device installable upstream to the energy consumingdevice. Therefore, the optimized load shape switch in any and allembodiments integrates processor into a device such as a computer, smartswitch, smart meter, thermostat, smart phone, an Internet router, agraphical user interface (GUI), cloud-based energy controller, cloudappliance, data center, dashboard, home energy management system, abattery, an electric vehicle/electric vehicle charger, an energytransformation device, water boiler, air conditioner, and an appliance,for example.

The optimized load shape switch in any and all embodiments configuresthe optimized load shape signal to maximize the utilization of one ormore non-renewable energy generators, and particularly to maximize theuse of renewable generator s while maximizing the efficiency ofnon-renewable (including thermal generators). The optimized load shapesignal is calculated, either at the supply side, demand side, or at aquasi-supply side such as a distributor of energy, and is employed byenergy consuming devices on the demand or consumer side. The resultinguse of power on the demand side, either as a single device, group ofdevices, or in the aggregate, such as on a feeder basis or larger regionor environment region or geography, results in a corresponding energydraw upstream on the supply side that translates into usage by thosegenerators. Those generators, particularly the non-renewable generatorsthat can be flexibly driven irrespective of natural events such as theweather or time of day, as a result are deployed on a steady statebasis, that is at their maximum efficiency for the demanded load, andneither are stated or stopped nor ramped up and down, causing wear andtear on the equipment as well as saving immense cost of energy inspinning up those assets. The renewable energy generators, those thatare not flexible (inflexible) or depend on the environment such as theweather or time of day, are then free or capable to generate energy attheir normal operating conditions and times, that is without strainscaused by over generation or over supply.

The optimized load shape switch processor in any and all embodimentsmodifies the switching signal based on when the energy-consuming deviceis online.

The optimized load shape switch processor in any and all embodimentsmodifies the switching signal further based on a re-apportionment of theoptimized load shape signal in accordance when the energy-consumingdevice is expected to be online.

The optimized load shape switch processor in any and all embodimentsmodifies the switching signal based on charging and/or discharging ofthe energy-consuming device.

The optimized load shape switch processor in any and all embodimentsgenerates the optimized load shaping signal based on a forecast signalthat forecasts load of the serving area, a pre-defined forecast signal,a model forecast, and predicted signal.

The optimized load shape switch processor in any and all embodimentsgenerates a signal indicating it is compliant with at least a portion ofthe optimized load shaping signal.

The optimized load shape switch processor in any and all embodimentsreceives a credit or token for complying with at least a portion of theoptimized load shape signal. The optimized load shape switch processorin any and all embodiments modifies the switching signal in accordancewith the credit or token. Credits or tokens may encourage and/ordiscourage (or allowing disallowing) energy consuming devices to operateat a targeted load. This may be based on weighting one or more portionsof the optimum load shape signal. Credits or tokens may be earned orpurchased by the consumer for operating energy consuming devices at theoptimized load shape. The credit or token in any and all embodiments isproduced corresponding to at least a portion of the optimized load shapesignal.

Various examples may be implemented using hardware elements, softwareelements, or a combination of both. In some examples, hardware elementsmay include devices, components, processors, microprocessors, circuits,circuit elements (e.g., transistors, resistors, capacitors, inductors,and so forth), integrated circuits, ASICs, PLDs, DSPs, FPGAs, memoryunits, logic gates, registers, semiconductor device, chips, microchips,chip sets, and so forth. In some examples, software elements may includesoftware components, programs, applications, computer programs,application programs, system programs, machine programs, operatingsystem software, middleware, firmware, software modules, routines,subroutines, functions, methods, procedures, software interfaces, APIs,instruction sets, computing code, computer code, code segments, computercode segments, words, values, symbols, or any combination thereof.Determining whether an example is implemented using hardware elementsand/or software elements may vary in accordance with any number offactors, such as desired computational rate, power levels, heattolerances, processing cycle budget, input data rates, output datarates, memory resources, data bus speeds and other design or performanceconstraints, as desired for a given implementation. It is noted thathardware, firmware and/or software elements may be collectively orindividually referred to herein as “module,” “logic,” “circuit,” or“circuitry.” A processor can be one or more combination of a hardwarestate machine, digital control logic, central processing unit, or anyhardware, firmware and/or software elements. A public utility company(or simply utility) may be considered an organization that maintains theinfrastructure for a public service (often also providing a serviceusing that infrastructure). Public utilities are typically subject toforms of public control and a regulation ranging from localcommunity-based groups to statewide government monopolies. A utility inany and all embodiments may include entities or companies that provideinfrastructure for the public service, including equipmentinfrastructure such as thermostats and meters/smart meters and softwareinfrastructure including software and analysis tools, Apps andinterfaces, forecasting tools, networks (internet or cloud), or other ITinfrastructure.

Some examples may be implemented using or as an article of manufactureor at least one computer-readable medium. A computer-readable medium mayinclude a non-transitory storage medium to store logic. In someexamples, the non-transitory storage medium may include one or moretypes of computer-readable storage media capable of storing electronicdata, including volatile memory or non-volatile memory, removable ornon-removable memory, erasable or non-erasable memory, writeable orre-writeable memory, and so forth. In some examples, the logic mayinclude various software elements, such as software components,programs, applications, computer programs, application programs, systemprograms, machine programs, operating system software, middleware,firmware, software modules, routines, subroutines, functions, methods,procedures, software interfaces, API, instruction sets, computing code,computer code, code segments, computer code segments, words, values,symbols, or any combination thereof.

According to some examples, a computer-readable medium may include anon-transitory storage medium to store or maintain instructions thatwhen executed by a machine, computing device or system, cause themachine, computing device or system to perform methods and/or operationsin accordance with the described examples. The instructions may includeany suitable type of code, such as source code, compiled code,interpreted code, executable code, static code, dynamic code, and thelike. The instructions may be implemented according to a predefinedcomputer language, manner or syntax, for instructing a machine,computing device or system to perform a certain function. Theinstructions may be implemented using any suitable high-level,low-level, object-oriented, visual, compiled and/or interpretedprogramming language.

One or more aspects of at least one example may be implemented byrepresentative instructions stored on at least one machine-readablemedium which represents various logic within the processor, which whenread by a machine, computing device or system causes the machine,computing device or system to fabricate logic to perform the techniquesdescribed herein. Such representations, known as “IP cores” may bestored on a tangible, machine readable medium and supplied to variouscustomers or manufacturing facilities to load into the fabricationmachines that actually make the logic or processor.

The appearances of the phrase “one example” or “an example” are notnecessarily all referring to the same example or embodiment. Any aspectdescribed herein can be combined with any other aspect or similar aspectdescribed herein, regardless of whether the aspects are described withrespect to the same figure or element. Division, omission or inclusionof block functions depicted in the accompanying figures does not inferthat the hardware components, circuits, software and/or elements forimplementing these functions would necessarily be divided, omitted, orincluded in embodiments.

Some examples may be described using the expression “coupled” and“connected” along with their derivatives. These terms are notnecessarily intended as synonyms for each other. For example,descriptions using the terms “connected” and/or “coupled” may indicatethat two or more elements are in direct physical or electrical contactwith each other. The term “coupled,” however, may also mean that two ormore elements are not in direct contact with each other, but yet stillco-operate or interact with each other.

The terms “first,” “second,” and the like, herein do not denote anyorder, quantity, or importance, but rather are used to distinguish oneelement from another. The terms “a” and “an” herein do not denote alimitation of quantity, but rather denote the presence of at least oneof the referenced items. The term “asserted” used herein with referenceto a signal denote a state of the signal, in which the signal is active,and which can be achieved by applying any logic level either logic 0 orlogic 1 to the signal. The terms “follow” or “after” can refer toimmediately following or following after some other event or events.Other sequences of steps may also be performed according to alternativeembodiments. Furthermore, additional steps may be added or removeddepending on the particular applications. Any combination of changes canbe used and one of ordinary skill in the art with the benefit of thisdisclosure would understand the many variations, modifications, andalternative embodiments thereof.

Disjunctive language such as the phrase “at least one of X, Y, or Z,”unless specifically stated otherwise, is otherwise understood within thecontext as used in general to present that an item, term, etc., may beeither X, Y, or Z, or any combination thereof (e.g., X, Y, and/or Z).Thus, such disjunctive language is not generally intended to, and shouldnot, imply that certain embodiments require at least one of X, at leastone of Y, or at least one of Z to each be present. Additionally,conjunctive language such as the phrase “at least one of X, Y, and Z,”unless specifically stated otherwise, should also be understood to meanX, Y, Z, or any combination thereof, including “X, Y, and/or Z.”

Illustrative examples of the devices, systems, and methods disclosedherein are provided below. An embodiment of the devices, systems, andmethods may include any one or more, and any combination of, theexamples described below.

What is claimed is:
 1. An apparatus generating a load shape signal, theapparatus comprising: a processor configured to: obtain a price ofenergy signal, the price of energy signal indicative of a price ofenergy provided on a power grid or micro-grid; generate the load shapesignal using a modification of the price of energy, the modificationbeing at least an inversion or partial inversion of the price of energyor at least a portion of the price of energy; and wherein the load shapesignal is indicative of a load that one or more appliances of energy areto at least attempt to achieve.
 2. The apparatus of claim 1, wherein thepricing signal is based on the price of energy selected from the groupconsisting of a forecast, wholesale, day-ahead, or real time pricingsignal.
 3. The apparatus of claim 1, wherein the processor is configuredto generate the load shape signal for the price of energy at aparticular moment or over time.
 4. The apparatus of claim 1, wherein theprocessor is configured to generate the load shape signal for the priceof energy based on parts of the price or pricing signal.
 5. Theapparatus of claim 1, wherein the processor is configured to generatethe load shape signal further expresses the load shape signal in termsof percentage use.
 6. A method for generating a load shape signal, themethod comprising: obtaining a price of energy signal, the price ofenergy signal indicative of a price of energy provided on a power gridor micro-grid; generating the load shape signal using a modification ofthe price of energy, the modification being at least an inversion orpartial inversion of the price of energy or at least a portion of theprice of energy; and wherein the load shape signal is indicative of aload that one or more appliances of energy are to at least attempt toachieve.
 7. The method of claim 6, wherein the pricing signal is basedon the price of energy selected from the group consisting of a forecast,wholesale, day-ahead, or real time pricing signal.
 8. The method ofclaim 6, wherein generating the load shape signal generates the loadshape signal for the price of energy at a particular moment or over time9. The method of claim 6, wherein generating the load shape signalgenerates the load shape signal for the price of energy based on partsof the price or pricing signal.
 10. The method of claim 6, whereingenerating the load shape signal generates the load shape signal furtherexpresses the load shape signal in terms of percentage use.
 11. Anapparatus receiving a load shape signal, the apparatus comprising: aprocessor configured to: obtain a load shape signal that is at least aninversion or partial inversion of a price of energy or at least aportion of the price of energy; wherein the load shape signal isindicative of a target load that is to be achieved; and adjust usage ofenergy based on the load shape signal to attempt to achieve the targetload.
 12. The apparatus of claim 11, wherein the pricing signal is basedon the price of energy selected from the group consisting of a forecast,wholesale, day-ahead, or real time pricing signal.
 13. The apparatus ofclaim 11, wherein the load shape signal is based on the price of energyat a particular moment or over time
 14. The apparatus of claim 11,wherein the load shape signal is based on the price of energy based onparts of the price or pricing signal.
 15. The apparatus of claim 11,wherein the load shape signal is expressed in terms of percentage use.16. The apparatus of claim 11, wherein the apparatus is selected fromthe group consisting of an appliance, an electric or autonomous vehicle,and a battery.
 17. A system that provides a load shape signal, theapparatus comprising: a processor configured to: obtain a price ofenergy signal, the price of energy signal indicative of a price ofenergy provided on a power grid or micro-grid; wherein the load shapesignal is generated using a modification of the price of energy, themodification being at least an inversion or partial inversion of theprice of energy or at least a portion of the price of energy; andwherein the load shape signal is indicative of a load that one or moreappliances of energy are to at least attempt to achieve.
 18. The systemof claim 17, wherein the pricing signal is based on the price of energyselected from the group consisting of a forecast, wholesale, day-ahead,or real time pricing signal.
 19. The system of claim 17, wherein theprocessor is configured to generate the load shape signal for the priceof energy at a particular moment or over time
 20. The system of claim17, wherein the processor is configured to generate the load shapesignal for the price of energy based on parts of the price or pricingsignal.
 21. The system of claim 17, wherein the processor is configuredto generate the load shape signal further expresses the load shapesignal in terms of percentage use.
 22. The system of claim 17, whereinthe system is selected from the group consisting of a power grid, autility resource supplier network, a wholesale provider network ofpower, and a distributor network of power.